Differential and Integral Equations

Multiple positive solutions of semilinear elliptic equations with weight function in exterior domains

Michinori Ishiwata

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Abstract

In this paper, we are concerned with the multiplicity of solutions for semilinear elliptic problems with weight functions in exterior domains. We prove that, if the decay of the weight function at spatial infinity is sufficiently slow, then the equation admits at least three solutions and two of them escape away to the spatial infinity as the decay rate of the weight function tends to $0$. The result is proved via the variational method combined with the Ljusternik--Schnirelman-type multiplicity theorem.

Article information

Source
Differential Integral Equations, Volume 26, Number 1/2 (2013), 183-200.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1355867513

Mathematical Reviews number (MathSciNet)
MR3058704

Zentralblatt MATH identifier
1289.35072

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space

Citation

Ishiwata, Michinori. Multiple positive solutions of semilinear elliptic equations with weight function in exterior domains. Differential Integral Equations 26 (2013), no. 1/2, 183--200. https://projecteuclid.org/euclid.die/1355867513


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