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Separating solutions of nonlinear problems using nonlinear generalized Rayleigh quotients. (English) Zbl 1484.35232

Summary: This paper deals with nonlinear elliptic boundary value problems with complicated geometry of nonlinearities. A new method for obtaining multiple solutions based on a recursive use of the nonlinear generalized Rayleigh quotients to the split Nehari manifold into subsets without degeneracies is introduced. The method is applied to prove the multiplicity result for nonnegative solutions, as well as to find a ground state of elliptic boundary value problems with nonlinearities of polynomial type.

MSC:

35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35J25 Boundary value problems for second-order elliptic equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A15 Variational methods applied to PDEs
Full Text: DOI

References:

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