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arXiv · 1807.03961

Existence results for Schr\"odinger $p(x)$-Laplace equations involving critical growth in $\mathbb{R}^N$

Ky Ho·Yun-Ho Kim·Inbo Sim
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Abstract

We establish some existence results for Schr\"odinger $p(x)$-Laplace equations in $\mathbb{R}^N$ with various potentials and critical growth of nonlinearity that may occur on some nonempty set, although not necessarily the whole space $\mathbb{R}^N$. The proofs are mainly based on concentration-compactness principles in a suitable weighted variable exponent Sobolev space and its imbeddings.

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Ky Ho, Yun-Ho Kim, Inbo Sim. 2018-07-11. Existence results for Schr\"odinger $p(x)$-Laplace equations involving critical growth in $\mathbb{R}^N$. https://arxiv.org/abs/1807.03961

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