Existence, nonexistence and multiplicity of positive solutions for the poly-Laplacian and nonlinearities with zeros

Autor:	Leonelo Iturriaga, Eugenio Massa
Rok vydání:	2018
Předmět:	Physics MÉTODOS VARIACIONAIS Pure mathematics Nonlinear system Applied Mathematics Bounded function Discrete Mathematics and Combinatorics Multiplicity (mathematics) Boundary value problem Laplace operator Analysis
Zdroj:	Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP
ISSN:	1553-5231
DOI:	10.3934/dcds.2018166
Popis:	In this paper we consider the equation \begin{document}$(-Δ)^k\, u = λ f(x, u)+μ g(x, u)$\end{document} with Navier boundary conditions, in a bounded and smooth domain. The main interest is when the nonlinearity is nonnegative but admits a zero and \begin{document}$f, g$\end{document} are, respectively, identically zero above and below the zero. We prove the existence of multiple positive solutions when the parameters lie in a region of the form \begin{document}$λ>\overline λ$\end{document} and \begin{document}$0 , then we provide further conditions under which, respectively, the bound \begin{document}$\overlineμ(λ)$\end{document} is either necessary, or can be removed.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b92945751cb61c9de7e96338fd385ff8 https://doi.org/10.3934/dcds.2018166 Zobrazit plný text záznamu