Taiwanese Journal of Mathematics

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

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 1 July 2017

https://projecteuclid.org/euclid.twjm/1498874450

Digital Object Identifier
doi:10.11650/tjm.20.2016.6173

Mathematical Reviews number (MathSciNet)
MR3481394

Zentralblatt MATH identifier
1357.35134

Citation

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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