Taiwanese Journal of Mathematics

Solutions for a $p(x)$-Kirchhoff Type Problem with a Non-smooth Potential in $\mathbb{R}^N$

Ziqing Yuan, Lihong Huang, and Chunyi Zeng

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This paper is concerned with a class of $p(x)$-Kirchhoff type problem in $\mathbb{R}^N$. By the theories of nonsmooth critical point and variable exponent Sobolev spaces, we establish the existence and multiplicity of solutions to the $p(x)$-Kirchhoff type problem under weaker hypotheses on the nonsmooth potential at zero (at infinity, respectively). Some recent results in the literature are generalized and improved.

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Taiwanese J. Math., Volume 20, Number 2 (2016), 449-472.

First available in Project Euclid: 1 July 2017

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Primary: 35J85 47J30: Variational methods [See also 58Exx] 49J52: Nonsmooth analysis [See also 46G05, 58C50, 90C56]

nonsmooth critical point locally Lipschitz $p(x)$-Kirchhoff type problem variational method


Yuan, Ziqing; Huang, Lihong; Zeng, Chunyi. Solutions for a $p(x)$-Kirchhoff Type Problem with a Non-smooth Potential in $\mathbb{R}^N$. Taiwanese J. Math. 20 (2016), no. 2, 449--472. doi:10.11650/tjm.20.2016.6173. https://projecteuclid.org/euclid.twjm/1498874450

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