Advances in Differential Equations

Existence of multiple sign-changing solutions for an asymptotically linear elliptic problem and the topology of the configuration space of the domain

Naoki Shioji

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Abstract

In the case $f \in C(\mathbb R,\mathbb R)$ is asymptotically linear, we give a lower estimate of number of sign-changing solutions to the problem $$-d^2 \Delta u + u =f(u)\;\;\text{in $\Omega$,}\quad u=0 \;\;\text{on $\partial\Omega$,} $$ where $\Omega$ is a bounded domain in $\\mathbb R^N$ ($N \geq 2$) and $d>0$ is an appropriate small number.

Article information

Source
Adv. Differential Equations Volume 17, Number 5/6 (2012), 471-510.

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703077

Mathematical Reviews number (MathSciNet)
MR2951938

Zentralblatt MATH identifier
1296.35066

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations

Citation

Shioji, Naoki. Existence of multiple sign-changing solutions for an asymptotically linear elliptic problem and the topology of the configuration space of the domain. Adv. Differential Equations 17 (2012), no. 5/6, 471--510. https://projecteuclid.org/euclid.ade/1355703077.


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