Nonlinear perturbed integral equations related to nonlocal boundary value problems

Abstract

By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example, when dealing with boundary value problems where nonlocal terms occur in the differential equation and/or in the boundary conditions. Some examples are given to illustrate the theoretical results.2010 Mathematics Subject Classification. Primary 45G10, secondary 34A34, 34B10, 34B15, 34B18, 34K10.

A topological approach to nonlocal elliptic partial differential equations on an annulus

“…A noteworthy contribution is that of Webb and Infante [49], who provided an elegant theory for studying all manner of nonlocal boundary conditions. Other interesting contributions have come from Anderson [2], Cabada, Infante, and Tojo, [7, 8], Cianciaruso, Infante, and Pietramala [10], Goodrich [17, 18], Graef and Webb [27], Infante [29], Infante and Pietramala [30–35], Jankowski [36], Karakostas and Tsamatos [37, 38], Karakostas [39], Webb [47], Webb and Infante [48, 50], and Yang [53–57]. The classical papers by Picone [43] and Whyburn [51] are interesting as concerns the original developments of differential equations with nonlocal elements.…”

Solutions of perturbed Hammerstein integral equations with applications

“…One possibility is to rewrite this BVP as a perturbed Hammerstein integral equation, that is (1.3) u(t) = γ(t)h(u(1)) + This kind of perturbed integral equation has been investigated in the past by a number of authors, we refer the reader to the manuscripts [1,6,8,21,24,25,27,29,34,50,71,89,90] and references therein.…”

Existence of Solutions of Integral Equations Defined in Unbounded Domains Via Spectral Theory

“…Analogously to the proof for L 1 , from (C 1 ), (ii), given ǫ ∈ + , there exists some δ ∈ + such that for t 1…”