English

Existence of multi-bump solutions for a class of elliptic problems involving the biharmonic operator

Analysis of PDEs 2016-08-06 v1

Abstract

Using variational methods, we establish existence of multi-bump solutions for the following class of problems {Δ2u+(λV(x)+1)u=f(u),\mboxinRN,uH2(RN), \left\{ \begin{array}{l} \Delta^2 u +(\lambda V(x)+1)u = f(u), \quad \mbox{in} \quad \mathbb{R}^{N}, u \in H^{2}(\mathbb{R}^{N}), \end{array} \right. where N1N \geq 1, Δ2\Delta^2 is the biharmonic operator, ff is a continuous function with subcritical growth and V:RNRV : \mathbb{R}^N \rightarrow \mathbb{R} is a continuous function verifying some conditions.

Keywords

Cite

@article{arxiv.1602.03112,
  title  = {Existence of multi-bump solutions for a class of elliptic problems involving the biharmonic operator},
  author = {Claudianor O. Alves and Alânnio B. Nóbrega},
  journal= {arXiv preprint arXiv:1602.03112},
  year   = {2016}
}