On a singular Kirchhoff type problems driven by p(⋅)-Laplacian operator

ABSTRACT

This work is devoted to introduce a new Hardy-type inequality related to $p(\cdot )$-Laplacian operator. Moreover, by using the Mountain Pass theorem and the Krasnoselskii's genus theory, we show the existence and infinite solutions to the $p(\cdot )$-Kirchhoff type problem with singular nonlinearity.

Keywords:

• Variable exponent
• $p(\cdot )$-Kirchhoff equation
• $p(\cdot )$-Laplacian operator
• critical point
• mountain pass theorem
• krasnoselskii's genus theory

2010 Mathematics Subject Classifications:

• 35D05
• 35J60
• 35J75

Acknowledgments

The authors would like to thank to the anonymous referee for his/her carefully reading the manuscript and valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).