Multiple nontrivial solutions for \(p\)-Laplacian equations with an asymmetric nonlinearity. (English) Zbl 1212.35082

Summary: In this paper we study a nonlinear Dirichlet problem driven by the \(p\)-Laplacian and a right-hand side nonlinearity which exhibits an asymmetric behavior near \(+\infty \) and \(-\infty \). Using variational techniques based on the mountain pass theorem and the second deformation theorem, we prove the existence of at least two nontrivial \(C^1\)-solutions, one of which is strictly positive.


35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35J60 Nonlinear elliptic equations
35J70 Degenerate elliptic equations