Professor Jeffrey Webb
- Honorary Senior Research Fellow (School of Mathematics & Statistics)
Publications
2024
Webb, J. R. L. and Lan, K. (2024) Fractional differential equations of Bagley-Torvik and Langevin type. Fractional Calculus and Applied Analysis, (doi: 10.1007/s13540-024-00292-2) (Early Online Publication)
2023
Lan, K. and Webb, J.R.L. (2023) A new Bihari inequality and initial value problems of first order fractional differential equations. Fractional Calculus and Applied Analysis, 26(3), pp. 962-988. (doi: 10.1007/s13540-023-00152-5)
2022
Webb, J. R.L. (2022) Compactness of nonlinear integral operators with discontinuous and with singular kernels. Journal of Mathematical Analysis and Applications, 509(2), 126000. (doi: 10.1016/j.jmaa.2022.126000)
2017
Webb, J.R.L. (2017) New fixed point index results and nonlinear boundary value problems. Bulletin of the London Mathematical Society, 49(3), pp. 534-547. (doi: 10.1112/blms.12055)
2012
Webb, J.R.L. (2012) Existence of positive solutions for a thermostat model. Nonlinear Analysis: Real World Applications, 13(2), pp. 923-938. (doi: 10.1016/j.nonrwa.2011.08.027)
2011
Webb, J. (2011) Positive solutions of a boundary value problem with integral boundary conditions. Electronic Journal of Differential Equations, 55, pp. 1-10.
2010
Webb, J.R.L. (2010) Positive solutions of some higher order nonlocal boundary value problems. Electronic Journal of Qualitative Theory of Differential Equations, Spec.(29), pp. 1-15.
Webb, J.R.L. (2010) Remarks on a non-local boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 72(2), pp. 1075-1077. (doi: 10.1016/j.na.2009.07.047)
Webb, J.R.L. (2010) Remarks on nonlocal boundary value problems at resonance. Applied Mathematics and Computation, 216(2), pp. 497-500. (doi: 10.1016/j.amc.2010.01.056)
Webb, J.R.L. (2010) Solutions of nonlinear equations in cones and positive linear operators. Journal of the London Mathematical Society, 82(2), pp. 420-436. (doi: 10.1112/jlms/jdq037)
2009
Graef, J.R. and Webb, J.R.L. (2009) Third order boundary value problems with nonlocal boundary conditions. Nonlinear Analysis, 71(5-6), pp. 1542-1551. (doi: 10.1016/j.na.2008.12.047)
Webb, J.R.L. (2009) Non-local conjugate type boundary value problems of higher order. Nonlinear Analysis, 71(5-6), pp. 1933-1940. (doi: 10.1016/j.na.2009.01.033)
Webb, J.R.L. and Zima, M. (2009) Multiple positive solutions of resonant and non-resonant nonlocal boundary value problems. Nonlinear Analysis: Theory, Methods and Applications, 71(3-4), pp. 1369-1378. (doi: 10.1016/j.na.2008.12.010)
Webb, J.R.L. (2009) Remarks on u 0-positive operators. Journal of Fixed Point Theory and Applications, 5(1), pp. 37-45. (doi: 10.1007/s11784-008-0093-2)
Webb, J.R.L. and Infante, G. (2009) Nonlocal boundary value problems of arbitrary order. Journal of the London Mathematical Society, 79(1), pp. 238-258. (doi: 10.1112/jlms/jdn066)
Webb, J.R.L. (2009) Boundary value problems with vanishing Green's function. Communications in Applied Analysis, 13,
Webb, J.R.L. (2009) Higher order non-local (n-1, 1) conjugate type boundary value problems. In: Cabada, A., Liz, E. and Nieto, J.J. (eds.) Mathematical Models In Engineering, Biology And Medicine. Series: AIP Conference Proceedings (1124). American Institute of Physics: Melville, NY, pp. 332-341. ISBN 978-0-7354-0660-5
Webb, J.R.L. and Infante, G. (2009) Semi-positone nonlocal boundary value problems of arbitrary order. Communications on Pure and Applied Analysis, 9(2), pp. 563-581. (doi: 10.3934/cpaa.2010.9.563)
2008
Webb, J.R.L., Infante, G. and Franco, D. (2008) Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 138(2), pp. 427-446. (doi: 10.1017/S0308210506001041)
Webb, J.R.L. (2008) Uniqueness of the principal eigenvalue in nonlocal boundary value problems. Discrete and Continuous Dynamical Systems: Series S, 1(1), pp. 177-186. (doi: 10.3934/dcdss.2008.1.177)
Webb, J.R.L. and Infante, G. (2008) Positive solutions of nonlocal boundary value problems involving integral conditions. No DEA - Nonlinear Differential Equations and Applications, 15(1-2), pp. 45-67. (doi: 10.1007/s00030-007-4067-7)
2007
Khan, R.A. and Webb, J.R.L. (2007) Existence of at least three solutions of nonlinear three point boundary value problems with super-quadratic growth. Journal of Mathematical Analysis and Applications, 328(1), pp. 690-698. (doi: 10.1016/j.jmaa.2006.05.074)
2006
Webb, J.R.L. and Infante, G. (2006) Positive solutions of nonlocal boundary value problems: a unified approach. Journal of the London Mathematical Society, 74(3), pp. 673-693. (doi: 10.1112/S0024610706023179)
Infante, G. and Webb, J.R.L. (2006) Nonlinear non-local boundary-value problems and perturbed Hammerstein integral equations. Proceedings of the Edinburgh Mathematical Society, 49(3), pp. 637-656. (doi: 10.1017/S0013091505000532)
Franco, D. and Webb, J.R.L. (2006) Collisionless orbits of singular and non singular dynamical systems. Discrete and Continuous Dynamical Systems: Series A, 15(3), pp. 747-757. (doi: 10.3934/dcds.2006.15.747)
Infante, G. and Webb, J.R.L. (2006) Loss of positivity in a nonlinear scalar heat equation. Nonlinear Differential Equations and Applications, 13(2), pp. 249-261. (doi: 10.1007/s00030-005-0039-y)
Khan, R.A. and Webb, J.R.L. (2006) Existence of at least three solutions of a second-order three-point boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 64(6), pp. 1356-1366. (doi: 10.1016/j.na.2005.06.040)
Khan, R.A. and Webb, J.R.L. (2006) Existence of at least two solutions of second order nonlinear three point boundary value problems. Dynamic Systems and Applications, 15, pp. 119-132.
Webb, J. and Lan, K. (2006) Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type. Topological Methods in Nonlinear Analysis, 27, pp. 91-115.
2005
Guo, Z.M. and Webb, J.R.L. (2005) Structure of boundary blow-up solutions for quasilinear elliptic problems I. Large and small solutions. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 135, pp. 615-642.
Guo, Z. and Webb, J. (2005) Structure of boundary blow-up solutions for quasi-linear elliptic problems II: small and intermediate solutions. Journal of Differential Equations, 211, pp. 187-217. (doi: 10.1016/j.jde.2004.06.008)
Webb, J.R.L. (2005) Multiple positive solutions of some nonlinear heat flow problems. Discrete and Continuous Dynamical Systems, Suppl., pp. 895-903.
Webb, J. (2005) Optimal constants in a nonlocal boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 63, pp. 672-685. (doi: 10.1016/j.na.2005.02.055)
2003
Guo, Z. and Webb, J. (2003) Profile of solutions with sharp layers to some singularly perturbed quasilinear Dirichlet problems. Communications in Contemporary Mathematics, 5, pp. 883-920.
Infante, G. and Webb, J. (2003) Positive solutions of some nonlocal boundary value problems. Abstract and Applied Analysis(18), pp. 1047-1060. (doi: 10.1155/S1085337503301034)
Webb, J.R.L. (2003) Extensions of Gronwall's inequality with logarithmic terms. In: Barletta, E. (ed.) Lecture notes of Seminario Interdisciplinare di Matematica. Dipartimento di Matematica, Universita degli Studi della Basilicata: Potenza, pp. 149-159.
Webb, J.R.L. (2003) Three-point boundary value problems with solutions that change sign. Journal of Integral Equations and Applications, 15(1), pp. 37-57. (doi: 10.1216/jiea/1181074944)
2002
Guo, Z. and Webb, J. (2002) Large and small solutions of a class of quasilinear elliptic eigenvalue problems. Journal of Differential Equations, 180, pp. 1-50. (doi: 10.1006/jdeq.2001.4049)
Infante, G. and Webb, J. (2002) A finite dimensional approach to nonlinear spectral theory. Nonlinear Analysis: Theory, Methods and Applications, 51, pp. 171-188.
Infante, G. and Webb, J. (2002) Nonzero solutions of Hammerstein integral equations with discontinuous kernels. Journal of Mathematical Analysis and Applications, 272, pp. 30-42.
Lan, K. and Webb, J. (2002) A-properness of contractive and condensing maps. Nonlinear Analysis: Theory, Methods and Applications, 49, pp. 885-895.
Webb, J.R.L. (2002) Remarks on positive solutions of some three point boundary value problems. In: Fourth International Conference on Dynamical Systems and Differential Equations, Wilmington, NC, 24-27 May, 2002, pp. 905-915.
2001
Webb, J. (2001) Positive solutions of some three point boundary value problems via fixed point index theory. Nonlinear Analysis: Theory, Methods and Applications, 47, pp. 4319-4332.
Articles
Webb, J. R. L. and Lan, K. (2024) Fractional differential equations of Bagley-Torvik and Langevin type. Fractional Calculus and Applied Analysis, (doi: 10.1007/s13540-024-00292-2) (Early Online Publication)
Lan, K. and Webb, J.R.L. (2023) A new Bihari inequality and initial value problems of first order fractional differential equations. Fractional Calculus and Applied Analysis, 26(3), pp. 962-988. (doi: 10.1007/s13540-023-00152-5)
Webb, J. R.L. (2022) Compactness of nonlinear integral operators with discontinuous and with singular kernels. Journal of Mathematical Analysis and Applications, 509(2), 126000. (doi: 10.1016/j.jmaa.2022.126000)
Webb, J.R.L. (2017) New fixed point index results and nonlinear boundary value problems. Bulletin of the London Mathematical Society, 49(3), pp. 534-547. (doi: 10.1112/blms.12055)
Webb, J.R.L. (2012) Existence of positive solutions for a thermostat model. Nonlinear Analysis: Real World Applications, 13(2), pp. 923-938. (doi: 10.1016/j.nonrwa.2011.08.027)
Webb, J. (2011) Positive solutions of a boundary value problem with integral boundary conditions. Electronic Journal of Differential Equations, 55, pp. 1-10.
Webb, J.R.L. (2010) Positive solutions of some higher order nonlocal boundary value problems. Electronic Journal of Qualitative Theory of Differential Equations, Spec.(29), pp. 1-15.
Webb, J.R.L. (2010) Remarks on a non-local boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 72(2), pp. 1075-1077. (doi: 10.1016/j.na.2009.07.047)
Webb, J.R.L. (2010) Remarks on nonlocal boundary value problems at resonance. Applied Mathematics and Computation, 216(2), pp. 497-500. (doi: 10.1016/j.amc.2010.01.056)
Webb, J.R.L. (2010) Solutions of nonlinear equations in cones and positive linear operators. Journal of the London Mathematical Society, 82(2), pp. 420-436. (doi: 10.1112/jlms/jdq037)
Graef, J.R. and Webb, J.R.L. (2009) Third order boundary value problems with nonlocal boundary conditions. Nonlinear Analysis, 71(5-6), pp. 1542-1551. (doi: 10.1016/j.na.2008.12.047)
Webb, J.R.L. (2009) Non-local conjugate type boundary value problems of higher order. Nonlinear Analysis, 71(5-6), pp. 1933-1940. (doi: 10.1016/j.na.2009.01.033)
Webb, J.R.L. and Zima, M. (2009) Multiple positive solutions of resonant and non-resonant nonlocal boundary value problems. Nonlinear Analysis: Theory, Methods and Applications, 71(3-4), pp. 1369-1378. (doi: 10.1016/j.na.2008.12.010)
Webb, J.R.L. (2009) Remarks on u 0-positive operators. Journal of Fixed Point Theory and Applications, 5(1), pp. 37-45. (doi: 10.1007/s11784-008-0093-2)
Webb, J.R.L. and Infante, G. (2009) Nonlocal boundary value problems of arbitrary order. Journal of the London Mathematical Society, 79(1), pp. 238-258. (doi: 10.1112/jlms/jdn066)
Webb, J.R.L. (2009) Boundary value problems with vanishing Green's function. Communications in Applied Analysis, 13,
Webb, J.R.L. and Infante, G. (2009) Semi-positone nonlocal boundary value problems of arbitrary order. Communications on Pure and Applied Analysis, 9(2), pp. 563-581. (doi: 10.3934/cpaa.2010.9.563)
Webb, J.R.L., Infante, G. and Franco, D. (2008) Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 138(2), pp. 427-446. (doi: 10.1017/S0308210506001041)
Webb, J.R.L. (2008) Uniqueness of the principal eigenvalue in nonlocal boundary value problems. Discrete and Continuous Dynamical Systems: Series S, 1(1), pp. 177-186. (doi: 10.3934/dcdss.2008.1.177)
Webb, J.R.L. and Infante, G. (2008) Positive solutions of nonlocal boundary value problems involving integral conditions. No DEA - Nonlinear Differential Equations and Applications, 15(1-2), pp. 45-67. (doi: 10.1007/s00030-007-4067-7)
Khan, R.A. and Webb, J.R.L. (2007) Existence of at least three solutions of nonlinear three point boundary value problems with super-quadratic growth. Journal of Mathematical Analysis and Applications, 328(1), pp. 690-698. (doi: 10.1016/j.jmaa.2006.05.074)
Webb, J.R.L. and Infante, G. (2006) Positive solutions of nonlocal boundary value problems: a unified approach. Journal of the London Mathematical Society, 74(3), pp. 673-693. (doi: 10.1112/S0024610706023179)
Infante, G. and Webb, J.R.L. (2006) Nonlinear non-local boundary-value problems and perturbed Hammerstein integral equations. Proceedings of the Edinburgh Mathematical Society, 49(3), pp. 637-656. (doi: 10.1017/S0013091505000532)
Franco, D. and Webb, J.R.L. (2006) Collisionless orbits of singular and non singular dynamical systems. Discrete and Continuous Dynamical Systems: Series A, 15(3), pp. 747-757. (doi: 10.3934/dcds.2006.15.747)
Infante, G. and Webb, J.R.L. (2006) Loss of positivity in a nonlinear scalar heat equation. Nonlinear Differential Equations and Applications, 13(2), pp. 249-261. (doi: 10.1007/s00030-005-0039-y)
Khan, R.A. and Webb, J.R.L. (2006) Existence of at least three solutions of a second-order three-point boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 64(6), pp. 1356-1366. (doi: 10.1016/j.na.2005.06.040)
Khan, R.A. and Webb, J.R.L. (2006) Existence of at least two solutions of second order nonlinear three point boundary value problems. Dynamic Systems and Applications, 15, pp. 119-132.
Webb, J. and Lan, K. (2006) Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type. Topological Methods in Nonlinear Analysis, 27, pp. 91-115.
Guo, Z.M. and Webb, J.R.L. (2005) Structure of boundary blow-up solutions for quasilinear elliptic problems I. Large and small solutions. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 135, pp. 615-642.
Guo, Z. and Webb, J. (2005) Structure of boundary blow-up solutions for quasi-linear elliptic problems II: small and intermediate solutions. Journal of Differential Equations, 211, pp. 187-217. (doi: 10.1016/j.jde.2004.06.008)
Webb, J.R.L. (2005) Multiple positive solutions of some nonlinear heat flow problems. Discrete and Continuous Dynamical Systems, Suppl., pp. 895-903.
Webb, J. (2005) Optimal constants in a nonlocal boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 63, pp. 672-685. (doi: 10.1016/j.na.2005.02.055)
Guo, Z. and Webb, J. (2003) Profile of solutions with sharp layers to some singularly perturbed quasilinear Dirichlet problems. Communications in Contemporary Mathematics, 5, pp. 883-920.
Infante, G. and Webb, J. (2003) Positive solutions of some nonlocal boundary value problems. Abstract and Applied Analysis(18), pp. 1047-1060. (doi: 10.1155/S1085337503301034)
Webb, J.R.L. (2003) Three-point boundary value problems with solutions that change sign. Journal of Integral Equations and Applications, 15(1), pp. 37-57. (doi: 10.1216/jiea/1181074944)
Guo, Z. and Webb, J. (2002) Large and small solutions of a class of quasilinear elliptic eigenvalue problems. Journal of Differential Equations, 180, pp. 1-50. (doi: 10.1006/jdeq.2001.4049)
Infante, G. and Webb, J. (2002) A finite dimensional approach to nonlinear spectral theory. Nonlinear Analysis: Theory, Methods and Applications, 51, pp. 171-188.
Infante, G. and Webb, J. (2002) Nonzero solutions of Hammerstein integral equations with discontinuous kernels. Journal of Mathematical Analysis and Applications, 272, pp. 30-42.
Lan, K. and Webb, J. (2002) A-properness of contractive and condensing maps. Nonlinear Analysis: Theory, Methods and Applications, 49, pp. 885-895.
Webb, J. (2001) Positive solutions of some three point boundary value problems via fixed point index theory. Nonlinear Analysis: Theory, Methods and Applications, 47, pp. 4319-4332.
Book Sections
Webb, J.R.L. (2009) Higher order non-local (n-1, 1) conjugate type boundary value problems. In: Cabada, A., Liz, E. and Nieto, J.J. (eds.) Mathematical Models In Engineering, Biology And Medicine. Series: AIP Conference Proceedings (1124). American Institute of Physics: Melville, NY, pp. 332-341. ISBN 978-0-7354-0660-5
Webb, J.R.L. (2003) Extensions of Gronwall's inequality with logarithmic terms. In: Barletta, E. (ed.) Lecture notes of Seminario Interdisciplinare di Matematica. Dipartimento di Matematica, Universita degli Studi della Basilicata: Potenza, pp. 149-159.
Conference Proceedings
Webb, J.R.L. (2002) Remarks on positive solutions of some three point boundary value problems. In: Fourth International Conference on Dynamical Systems and Differential Equations, Wilmington, NC, 24-27 May, 2002, pp. 905-915.