Existence and multiplicity results for Kirchhoff type problems on a double phase setting

Abstract

In this paper, we study two classes of Kirchhoff type problems set on a double phase framework. That is, the functional space where finding solutions coincides with the Musielak-Orlicz-Sobolev space $W_0^{1,\mathcal{H}}(\Omega )$, with modular function $\mathcal{H}$ related to the so called double phase operator. Via a variational approach, we provide existence and multiplicity results.