A bifurcation and multiplicity result for a critical growth elliptic problem

Said El Manouni; Kanishka Perera

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arXiv · 2408.14755

A bifurcation and multiplicity result for a critical growth elliptic problem

Said El Manouni·Kanishka Perera

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Abstract

We consider a Br\'ezis-Nirenberg type critical growth $p$-Laplacian problem involving a parameter $\mu > 0$ in a smooth bounded domain $\Omega$. We prove the existence of multiple nontrivial solutions if either $\mu$ or the volume of $\Omega$ is sufficiently small. The proof is based on an abstract critical point theorem that only assumes a local $(\text{PS})$ condition. Our results are new even in the semilinear case $p = 2$.

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Said El Manouni, Kanishka Perera. 2024-08-27. A bifurcation and multiplicity result for a critical growth elliptic problem. https://arxiv.org/abs/2408.14755

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