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Infinitely many solutions for semilinear elliptic problems with sign-changing weight functions:
Stockholm University, Faculty of Science, Department of Mathematics.
2014 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 4, 756-770 p.Article in journal (Refereed) Published
##### Abstract [en]

In this paper we study the elliptic problem\begin{equation*} \left\{\begin{array}{ll} -\Delta u+u = a(x)|u|^{p-2}u+b(x)|u|^{q-2}u,\\ u\in H^{1}(\mathbb{R}^{N}),\end{array}\right.\end{equation*}where $2^{*}$ is the critical Sobolev exponent, $2< p<q< 2^{*}$and $a$ or $b$ is a sign-changing function. Under different assumptions on $a$ and $b$ we prove the existenceof infinitely many solutions to the above problem. We also show that one of these solutions is positive.

##### Place, publisher, year, edition, pages
2014. Vol. 93, no 4, 756-770 p.
##### Keyword [en]
Elliptic problem; sign-changing weight function; infinitely many solutions; positive solution; Nehari manifold
##### National Category
Mathematical Analysis
Mathematics
##### Identifiers
ISI: 000334052500005OAI: oai:DiVA.org:su-102353DiVA: diva2:709767
##### Funder
Swedish Research Council
##### Note

AuthorCount:2;

Available from: 2014-04-03 Created: 2014-04-03 Last updated: 2014-06-23Bibliographically approved

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