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On some classes of generalized Schrödinger equations. (English) Zbl 1465.35136

Summary: Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least \(1 + \sum_{i=2}^m \dim V_{ \lambda_i}\) pairs of nontrivial solutions if a parameter involved in the equation is large enough, where \(V_{\lambda_i}\) denotes the eigenspace associated to the \(i\)-th eigenvalue \(\lambda_i\) of Laplacian operator with homogeneous Dirichlet boundary condition.

MSC:

35J10 Schrödinger operator, Schrödinger equation
35J62 Quasilinear elliptic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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