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

Full-text: Open access

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

Permanent link to this document
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

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

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

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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