Existence and multiplicity of solutions for $m(x)-$polyharmonic elliptic Kirchhoff type equations without Ambrosetti-Rabinowitz conditions
Mohamed Karim Hamdani,
Abdellaziz Harrabi
Abstract:In this paper, we prove the existence of infinitely many solutions for a class of quasilinear elliptic m(x)polyharmonic Kirchhoff equations where the nonlinear function has a quasicritical growth at infinity and without assuming the Ambrosetti and Rabinowitz type condition. The new aspect consists in employing the notion of a Schauder basis to verify the geometry of the symmetric mountain pass theorem. Furthermore, for the case m(x) ≡ Const, we introduce a positive quantity λ M similar to the first eigenvalue … Show more
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