Juntao Sun, Tsung-Fang Wu
In this article, we study a class of generalized extensible beam equations with a superlinear nonlinearity
where , with and , is a parameter, and . Unlike most other papers on this problem, we allow the constant to be non-positive, which has the physical significance. Under some suitable assumptions on and , when is small and is large enough, we prove the existence of two nontrivial solutions and , one of which will blow up as the nonlocal term vanishes. Moreover, and strongly in as , where are two nontrivial solutions of Dirichlet BVPs on the bounded domain . Also, the nonexistence of nontrivial solutions is also obtained for large enough.
Submitted December 1, 2018. Published March 19, 2019.
Math Subject Classifications: 35J30, 35J35.
Key Words: Extensible beam equations; nontrivial solution; multiplicity; concentration of solutions.
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| Juntao Sun |
School of Mathematics and Statistics
Shandong University of Technology
Zibo 255049, China
| Tsung-Fang Wu |
Department of Applied Mathematics
National University of Kaohsiung
Kaohsiung 811, Taiwan
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