English

Existence and non-existence of Blow-up solutions for a non-autonomous problem with indefinite and gradient terms

Analysis of PDEs 2015-06-19 v1

Abstract

We deal with existence and non-existence of non-negative entire solutions that blow-up at infinity for a quasilinear problem depending on a non-negative real parameter. Our main objectives in this paper are to provide far more general conditions for existence and non-existence of solutions. To this end, we explore an associated μ\mu-parameter convective ground state problem, sub and super solutions method combined and an approximation arguments to show existence of solutions. To show the result of non-existence of solutions, we follow an idea due to Mitidieri-Pohozaev.

Keywords

Cite

@article{arxiv.1404.5751,
  title  = {Existence and non-existence of Blow-up solutions for a non-autonomous problem with indefinite and gradient terms},
  author = {Claudianor O. Alves and Carlos A. Santos and Jiazheng Zhou},
  journal= {arXiv preprint arXiv:1404.5751},
  year   = {2015}
}