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

Kanishka Perera

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arXiv · 2210.13742

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

Kanishka Perera

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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 $p = 2$.

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Kanishka Perera. 2022-10-25. A general perturbation theorem with applications to nonhomogeneous critical growth elliptic problems. https://arxiv.org/abs/2210.13742

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