| Abstract: |
| In this talk I will present our results on stationary Schr\{o}dinger equations, Schr\{o}dinger-Poisson systems, quasilinear Schr\{o}dinger equations and other related problems such as the Schr\{o}dinger-Kirchhoff equations. In all these problems the Schr\{o}dinger operator is indefinite, thus the zero function is not a local minimizer of the variational functional and the mountain pass theorem is not applicable. It is important to observed that except for the semilinear Schr\{o}dinger equation, the classical linking theorem is also not applicable. To overcome this difficulty we employ the concept of local linking (introduced by Shujie Li and Jiaquan Liu in the 1980`s), nontrivial solutions for these indefinite problems are obtained by variational methods. |
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