Parametric Robin double phase problems with critical growth on the boundary

Abstract

<p style='text-indent:20px;'>The aim of this paper is to study a double phase problem with nonlinear boundary condition of critical growth and with a superlinear right-hand side that does not satisfy the Ambrosetti-Rabinowitz condition. Based on an equivalent norm in the Musielak-Orlicz Sobolev space along with variational tools and critical point theory, we prove the existence of at least two nontrivial, bounded weak solutions.</p>