Nontrivial solutions of Kirchhoff type problems

SUN Juan; LIU Shibo

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Nontrivial solutions of Kirchhoff type problems

SUN Juan,LIU Shibo

Department of Mathematics, Shantou University

*Correspondence author

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Funding: Supported by RFDP （No.20094402110001）

Opened online:25 May 2011

Accepted by: none

Citation: SUN Juan,LIU Shibo.Nontrivial solutions of Kirchhoff type problems[OL]. [25 May 2011] http://en.paper.edu.cn/en_releasepaper/content/4428288

In this paper, we study Kirchhoff type problems on a bounded domain. We consider the cases that the nonlinearity is superlinear near zero but asymptotically 4-linear at infinity, and the nonlinearity is asymptotically linear near zero but 4-superlinear at infinity. By computing the relevant critical groups, we obtain nontrivial solutions via Morse theory.

Keywords:Kirchhoff type problems; eigenvalues; critical groups; critical points

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