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In this paper we study quasilinear elliptic equations driven by the so-calleddouble phase operator and with a nonlinear boundary condition. Due to the lackof regularity, we prove the existence of multiple solutions by applying theNehari manifold method along with truncation and comparison techniques andcritical point theory. In addition, we can also determine the sign of thesolutions (one positive, one negative, one nodal). Moreover, as a result ofindependent interest, we prove for a general class of such problems theboundedness of weak solutions.

Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold