Spike solutions for a class of singularly perturbed quasilinear elliptic equations

Marco Squassina

Spike solutions for a class of singularly perturbed quasilinear elliptic equations

Analysis of PDEs 2007-05-23 v1

Authors: Marco Squassina

Abstract

By means of a penalization scheme due to del Pino and Felmer, we prove the existence of single-peaked solutions for a class of singularly perturbed quasilinear elliptic equations associated with functionals which lack of smoothness. We don't require neither uniqueness assumptions on the limiting autonomous equation nor monotonicity conditions on the nonlinearity. Compared with the semilinear case some difficulties arise and the study of concentration of the solutions needs a somewhat involved analysis in which the Pucci-Serrin variational identity plays an important role.

Keywords

singularly perturbed quasilinear elliptic equations spike solutions penalization scheme lack of smoothness pucci-serrin variational identity concentration of solutions

Cite

@article{arxiv.math/0303006,
  title  = {Spike solutions for a class of singularly perturbed quasilinear elliptic equations},
  author = {Marco Squassina},
  journal= {arXiv preprint arXiv:math/0303006},
  year   = {2007}
}

Comments

will appear in: Nonlinear Anal. TMA

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