Kyoto Journal of Mathematics

Multiple solutions for asymptotically linear elliptic equations with sign-changing weight

Nikolaos S. Papageorgiou and Vicenţiu D. Rădulescu

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Abstract

We consider a semilinear Dirichlet problem driven by the Laplacian and with an indefinite (that is, sign-changing) weight and a nonlinearity which is asymptotically linear near ±. Using variational methods together with truncation techniques and Morse theory, we show that the problem has at least three nontrivial solutions, two of which have constant sign (one positive and the other negative).

Article information

Source
Kyoto J. Math., Volume 55, Number 3 (2015), 593-606.

Dates
Received: 12 February 2014
Revised: 30 June 2014
Accepted: 3 July 2014
First available in Project Euclid: 9 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1441824038

Digital Object Identifier
doi:10.1215/21562261-3089082

Mathematical Reviews number (MathSciNet)
MR3395980

Zentralblatt MATH identifier
1333.35026

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations
Secondary: 35J60: Nonlinear elliptic equations 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Keywords
indefinite weight weighted eigenvalue problem critical groups maximum principle mountain pass theorem

Citation

Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D. Multiple solutions for asymptotically linear elliptic equations with sign-changing weight. Kyoto J. Math. 55 (2015), no. 3, 593--606. doi:10.1215/21562261-3089082. https://projecteuclid.org/euclid.kjm/1441824038


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