Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-2449Articles in Press20240520An existence result for a Robin problem involving $p(x)$-Kirchhoff-type equation with indefinite weight541210.22060/ajmc.2024.22990.1213ENMehdiLatifiDepartment of Basic Sciences, Khatam-Ol-Anbia (PBA) University, Tehran, IranMohsenAlimohammadyDepartment of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar 47416-1468, IranJournal Article20240215This 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.