Eigenvalues of Elliptic Functional Differential Systems via a Birkhoff–Kellogg Type Theorem

Autor:	Gennaro Infante
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	positive solution nonlocal elliptic system functional boundary condition cone Birkhoff-Kellogg type theorem Mathematics QA1-939
Zdroj:	Mathematics, Vol 9, Iss 1, p 4 (2020)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math9010004
Popis:	Motivated by recent interest on Kirchhoff-type equations, in this short note we utilize a classical, yet very powerful, tool of nonlinear functional analysis in order to investigate the existence of positive eigenvalues of systems of elliptic functional differential equations subject to functional boundary conditions. We obtain a localization of the corresponding non-negative eigenfunctions in terms of their norm. Under additional growth conditions, we also prove the existence of an unbounded set of eigenfunctions for these systems. The class of equations that we study is fairly general and our approach covers some systems of nonlocal elliptic differential equations subject to nonlocal boundary conditions. An example is presented to illustrate the theory.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/a186b689aabd439b938dffa9a0c1e757 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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