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Title: Existence and multiplicity results for some eigenvalue generalized Hammerstein equations
Authors: López-Somoza, Lucía
Minhós, Feliz
Keywords: Hammerstein equations
Parameter dependence
Degree theory
Fixed points in cones
Issue Date: 7-Oct-2019
Publisher: Springer Open
Citation: López-Somoza, L., Minhós, F. Existence and multiplicity results for some generalized Hammerstein equations with a parameter. Adv Differ Equ 2019, 423 (2019).
Abstract: This paper considers the existence and multiplicity of fixed points for an integral operatorwith a positive parameter. The existence of solutions for these Hammerstein equations is obtained by fixed point index theory on new type of cones. Therefore some assumptions must hold only for, at least, one of the derivatives of the kernel or, even, for the kernel on a subset of the domain. Assuming some asymptotic conditions on the nonlinearity f, we get sufficient conditions for multiplicity of solutions. Two examples will illustrate the potentialities of the main results, namely the fact that the kernel function and/or some derivatives may only be positive on some subintervals, which can degenerate to a point. Moreover, an application of our method to general Lidstone problems improves the existent results in the literature in this field.
ISSN: 1687-1847 (electronic)
Type: article
Appears in Collections:MAT - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica
CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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