Existence and Multiplicity of Solutions for Schrödinger-Kirchhoff-Type Equations Involving the Fractional p(x,·)-Laplacian Without the (AR) Condition

چکیده مقاله

The purpose of this paper is to investigate the existence and multiplicity of weak solutions for a Kirchhoff-type problems driven by the non-local integro-differential operator of elliptic type (Formula Presented) where (Formula Presented) is a non-local operator with singular kernel K, Ω is an open bounded subset of ‚R^N with Lipschitz boundary ‚∂Ω, M is a continuous function and f is a Carath√©odory function. Under suitable assumptions on f(x,u) without (AR) condition, the existence and multiplicity solutions for the problem is obtained by using the Mountain Pass Theorem and the Fountain Theorem. © Soc. Paran. de Mat.