An existence result for a Robin problem involving $p(x)$-Kirchhoff-type equation with indefinite weight

Latifi, Mehdi; Alimohammady, Mohsen

doi:10.22060/ajmc.2024.22990.1213

An existence result for a Robin problem involving $p(x)$-Kirchhoff-type equation with indefinite weight

Document Type : Original Article

Authors

Mehdi Latifi ¹
Mohsen Alimohammady ²

¹ Department of Basic Sciences, Khatam-Ol-Anbia (PBA) University, Tehran, Iran

² Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar 47416-1468, Iran

10.22060/ajmc.2024.22990.1213

Abstract

This paper discusses the existence of nontrivial weak solutions for a class of $p(x)$-Kirchhoff-type equation plus an indefinite potential under Robin boundary condition. The variable exponent theory of generalized Lebesgue-Sobolev spaces, mountain pass theorem and Ekeland variational principle are used for this purpose.

Keywords