The existence of nontrivial solutions to a class of quasilinear equations (Q2030040)

Summary: In this paper, we study the following quasilinear equation: \(-\operatorname{div}(\phi (|\nabla u|) \nabla u)+\phi (|u|)u=f(u)\text{ in } \mathbb{R}^N\), where \(\phi\in C^1(\mathbb{R}^+ , \mathbb{R}^+)\) and \(\Phi (t)= \int_0^ts\phi (|s|)ds\). In the Orlicz-Sobolev space, by variational methods and a minimax theorem, we prove the equation has a nontrivial solution.