A general perturbation theorem with applications to nonhomogeneous critical growth elliptic problems

Kanishka Perera

A general perturbation theorem with applications to nonhomogeneous critical growth elliptic problems

Analysis of PDEs 2022-10-26 v1

Authors: Kanishka Perera

Abstract

We prove a general perturbation theorem that can be used to obtain pairs of nontrivial solutions of a wide range of local and nonlocal nonhomogeneous elliptic problems. Applications to critical $p$ -Laplacian problems, $p$ -Laplacian problems with critical Hardy-Sobolev exponents, critical fractional $p$ -Laplacian problems, and critical $(p,q)$ -Laplacian problems are given. Our results are new even in the semilinear case $p = 2$ .

Keywords

perturbation theorem elliptic problems nonhomogeneous critical growth p-laplacian hardy-sobolev fractional p-laplacian

Cite

@article{arxiv.2210.13742,
  title  = {A general perturbation theorem with applications to nonhomogeneous critical growth elliptic problems},
  author = {Kanishka Perera},
  journal= {arXiv preprint arXiv:2210.13742},
  year   = {2022}
}

Comments

arXiv admin note: text overlap with arXiv:2102.09131

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