English

Multi-bump solutions for a Kirchhoff problem type

Analysis of PDEs 2015-07-28 v1

Abstract

In this paper, we are going to study the existence of solution for the following Kirchhoff problem {M(R3u2dx+R3λa(x)+1)u2dx)(Δu+(λa(x)+1)u)=f(u)\mboxinR3,\mboxuH1(R3). \left\{ \begin{array}{l} M\biggl(\displaystyle\int_{\mathbb{R}^{3}}|\nabla u|^{2} dx +\displaystyle\int_{\mathbb{R}^{3}} \lambda a(x)+1)u^{2} dx\biggl) \biggl(- \Delta u + (\lambda a(x)+1)u\biggl) = f(u) \mbox{ in } \,\,\, \mathbb{R}^{3}, \\ \mbox{}\\ u \in H^{1}(\mathbb{R}^{3}). \end{array} \right. Assuming that the nonnegative function a(x)a(x) has a potential well with int(a1({0}))int (a^{-1}(\{0\})) consisting of kk disjoint components Ω1,Ω2,.....,Ωk\Omega_1, \Omega_2, ....., \Omega_k and the nonlinearity f(t)f(t) has a subcritical growth, we are able to establish the existence of positive multi-bump solutions by variational methods.

Keywords

Cite

@article{arxiv.1507.07361,
  title  = {Multi-bump solutions for a Kirchhoff problem type},
  author = {Claudianor O. Alves and Giovany M. Figueiredo},
  journal= {arXiv preprint arXiv:1507.07361},
  year   = {2015}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1501.02930

R2 v1 2026-06-22T10:19:18.505Z