Existence and multiplicity results for critical anisotropic Kirchhoff-type problems with nonlocal nonlinearities

Abstract

In this paper, we are interested in existence and multiplicity of solutions to anisotropic elliptic equations of Kirchhoff-type given by where Ω is a smooth bounded domain of and are parameters, where is the critical exponent and . The function is only continuous with and can change its sign, is a function with subcritical growth and Under appropriate assumptions on f, applying an adequate truncation argument on M and the Concentration Compactness-Principle for the anisotropic operator [1], we obtain the existence of a nontrivial solution for by the Mountain Pass Theorem [2] and multiplicity of solutions by Krasnoselskii's genus and the symmetric Mountain Pass Lemma [3]. As a model case for M and f, we can consider or with and with and appropriate