Solutions of perturbed Hammerstein integral equations with applications

Abstract

By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical results, we study some problems that occur in applied mathematics, namely models of chemical reactors, beams and thermostats. We also apply our theory in order to prove the existence of nontrivial radial solutions of systems of elliptic boundary value problems subject to nonlocal, nonlinear boundary conditions.

39 pages. arXiv admin note: text overlap with arXiv:1408.0170

References in corpus (3)

• Nonzero radial solutions for a class of elliptic systems with nonlocal BCs on annular domains
• Non-trivial solutions of local and non-local Neumann boundary-value problems
• Nonlinear perturbed integral equations related to nonlocal boundary value problems

Cited by in corpus (9)

• Nonzero positive solutions of nonlocal elliptic systems with functional BCs
• Nonzero positive solutions of elliptic systems with gradient dependence and functional BCs
• Nontrivial solutions of systems of perturbed Hammerstein integral equations with functional terms
• Nonzero radial solutions for elliptic systems with coupled functional BCs in exterior domains
• Positive and increasing solutions of perturbed Hammerstein integral equations with derivative dependence
• On the solvability of a parameter-dependent cantilever-type BVP
• Positive solutions of systems of perturbed Hammerstein integral equations with arbitrary order dependence
• On fourth order retarded equations with functional boundary conditions: a unified approach
• A Unified Topological Analysis of Variable Growth Kirchhoff-Type Equations