English

Kirchhoff-type problems involving subcritical and superlinear nonlinearities satisfying no further condition

Analysis of PDEs 2017-10-18 v2 Optimization and Control

Abstract

In this note, we deal with a problem of the type \cases {-h\left ( \int_{\Omega}|\nabla u(x)|^2dx\right ) \Delta u=f(u) & in $\Omega$\cr & \cr u_{|\partial\Omega}=0\ .\cr} As an application of a new general multiplicity result, we establish the existence of at least three solutions, two of which are global minima of the related energy functional. The only condition assumed on ff is that it be subcritical and superlinear: no condition on the behaviour of ff at 00 is requested.

Keywords

Cite

@article{arxiv.1710.05676,
  title  = {Kirchhoff-type problems involving subcritical and superlinear nonlinearities satisfying no further condition},
  author = {Biagio Ricceri},
  journal= {arXiv preprint arXiv:1710.05676},
  year   = {2017}
}