On some classes of generalized Schrödinger equations

Abstract

Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + ∑i=2m$\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

Keywords

• generalized schrödinger problems
• multiplicity of solutions
• nehari manifold
• 35j10
• 35j25
• 35j60