Existence, nonexistence and multiplicity of positive solutions for the poly-Laplacian and nonlinearities with zeros
type: Item
instance of: scholarly article
title: Existence, nonexistence and multiplicity of positive solutions for the poly-Laplacian and nonlinearities with zeros
zbMATH Open document ID: 1412.35146
author: Leonelo Iturriaga
author: Eugenio Massa
published in: Discrete and Continuous Dynamical Systems
publication date: 2018-08-16T00:00:00Z
review text: The following problem is considered. \[ \begin{cases} (-\Delta)^k u = \lambda f(x,u) + \mu g(x,u) & \text{in} \ \Omega,\\ u>0 & \text{in} \ \Omega, \\ (-\Delta)^i u = 0 & \text{on} \ \partial\Omega, \ i=0,\dots,k-1 \end{cases},\] where $\Omega$ is a bounded domain in $\mathbb{R}^N$ with smooth boundary, $\lambda$ and $\mu$ are nonnegative parameters, $f$ and $g$ are nonnegative functions and $k \in\mathbb{N}$. The regions of two parameters $(\lambda,\mu)$ for the existence, nonexistence and multiplicity of positive solutions are obtained.
reviewed by: Satoshi Tanaka
Mathematics Subject Classification ID: 35J91
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
zbMATH DE Number: 6919398
zbMATH Keywords: poly-Laplacian
zbMATH Keywords: existence and nonexistence of solutions
zbMATH Keywords: multiplicity of solutions
MaRDI profile type: Publication
full work available at URL: dcds.2018166
OpenAlex ID: W2808259922
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Wikidata QID: Q129695836
DOI: 10.3934/DCDS.2018166
description: scientific article; zbMATH DE number 6919398