Existence and multiplicity of solutions for generalized asymptotically linear Schrödinger-Kirchhoff equations. (English) Zbl 1484.35036
Summary: In this paper, we investigate the nonlinear Schrödinger-Kirchhoff equations on the whole space. By using the Morse index of the reduced Schrödinger operator, we show the existence and multiplicity of solutions for this problem with asymptotically linear nonlinearity via variational methods.
MSC:
| 35B33 | Critical exponents in context of PDEs |
| 35B35 | Stability in context of PDEs |
| 49R05 | Variational methods for eigenvalues of operators |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
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