Multiplicity theorems for the Dirichlet problem involving the \(p\)-Laplacian.
type: Item
instance of: scholarly article
title: Multiplicity theorems for the Dirichlet problem involving the \(p\)-Laplacian.
zbMATH Open document ID: 1163.35367
DOI: 10.1016/S0362-546X(03)00027-0
author: Gabriele Bonanno
author: R. Livrea
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-06-17T00:00:00Z
review text: Let \(\Omega\) be an open bounded domain in \(\mathbb R^N\) \((N\geq 1)\), \(p>N\), \(\lambda>0\) and \(f:\Omega\times\mathbb R\to\mathbb R\) is a Carathéodory function. The authors interested existence result for the following Dirichlet problem: \[ \Delta_pu+ \lambda f(x,u)=0 \quad\text{in }\Omega, \qquad u=0\quad\text{on }\partial\Omega, \tag{1} \] where \(\Delta_p\) is the \(p\)-Laplacian. Using variational methods the authors prove the existence of at least three weak solutions for (1) in \(W_0^{1,p}(\Omega)\).
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 1929505
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: multiple solutions
zbMATH Keywords: critical points
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1929505