Multiple solutions for semilinear elliptic equations in unbounded cylinder domains. (English) Zbl 1152.35371
Summary: In this paper, we show that if in and there exist positive constants such that for uniformly for where with , , , , , , a bounded domain and , then the Dirichlet problem in has a solution that changes sign in , in addition to a positive solution.
|35J60||Nonlinear elliptic equations|
|35J20||Second order elliptic equations, variational methods|
|35J25||Second order elliptic equations, boundary value problems|
|47J30||Variational methods (nonlinear operator equations)|