English

Existence of multi-bump solutions to biharmonic operator with critical exponential growth in $\mathbb{R}^4$

Analysis of PDEs 2016-03-21 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),\mboxinR4,uH2(R4), \left\{ \begin{array}{l} \Delta^2 u +(\lambda V(x)+1)u = f(u), \quad \mbox{in} \quad \mathbb{R}^{4}, u \in H^{2}(\mathbb{R}^{4}), \end{array} \right. where Δ2\Delta^2 is the biharmonic operator, ff is a continuous function with critical exponential growth and V:R4RV : \mathbb{R}^4 \rightarrow \mathbb{R} is a continuous function verifying some conditions.

Keywords

Cite

@article{arxiv.1603.05946,
  title  = {Existence of multi-bump solutions to biharmonic operator with critical exponential growth in $\mathbb{R}^4$},
  author = {Alânnio B. Nóbrega and Denilson S. Pereira},
  journal= {arXiv preprint arXiv:1603.05946},
  year   = {2016}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1602.03112