Multiple solutions for prescribed boundary value problem
type: Item
instance of: scholarly article
title: Multiple solutions for prescribed boundary value problem
zbMATH Open document ID: 1157.35365
DOI: 10.1016/S0362-546X(01)00844-6
author: Yuanji Cheng
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-09-30T00:00:00Z
review text: This paper deals with the semilinear elliptic boundary value problem \[ \begin{gathered} -\Delta u= f(x,u)\quad\text{in }\Omega,\\ u= g\quad\text{on }\partial\Omega\end{gathered} \] and the corresponding Bolza problem \(\ddot x+\nabla V(t,x)= 0\), \(0\leq t\leq T\), \(x(0)= x_0\), \(x(T)= x_1\), where \(\Omega\) is a bounded subset in \(\mathbb R^N\) with \(C^2\) boundary and \(g\) is a given continuous function on the boundary of \(\Omega\). Note that the most results in the literature are stated for the cases \(f(x,u)= |u|^{p-1}u+ h(x)\) or the time-independent systems \(V(t,x)= \widetilde V(x)+ h(t)\cdot x\), so the main goal of the author is to generalize the above-mentioned cases to the \(x\)-variable dependent variable nonlinearity \(f(x,u)\) and the fully time-dependent systems.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 47J30
zbMATH DE Number: 1810006
zbMATH Keywords: semilinear elliptic boundary value problem
MaRDI profile type: Publication
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full work available at URL: s0362-546x(01)00844-6
OpenAlex ID: W2007521844
description: scientific article; zbMATH DE number 1810006