Multiplicity results for a class of $p(x)$-Kirchhoff type equations with combined nonlinearities

Abstract

Using the mountain pass theorem combined with the Ekeland variational principle, we obtain at least two distinct, non-trivial weak solutions for a class of $p(x)$-Kirchhoff type equations with combined nonlinearities. We also show that the similar results can be obtained in the case when the domain has cylindrical symmetry.

Keywords

• $p(x)$-kirchhoff type operator
• multiple solutions
• mountain pass theorem
• ekeland's principle