Multiple Solutions For Some Strongly Indefinite Schr?dinger Type Equations

The main research work of this paper is as follows:1. The following Schrodinger-Poisson system in R3 with a strongly indefinite potential is studied. Its variational functional does not satisfy the global linking geometry under our assumptions. We obtain a nontrivial solution and, in case of odd nonlinearity, infinitely many solutions by using the local linking theorem and improved fountain theorem, respectively.2. The following Schrodinger-Kirchhoff type equation in RN with a strongly indefinite potential is studied. We don’t impose any conditions on the function g at infinity. We obtain infinitely many solutions by using a truncation method, the extension of Clark’s theorem and elliptic regularity theorem.3. The following sublinear Schrodinger equation in RN with a strongly indefinite potential is studied, while N≥3 and the potential V3 is 1-periodic with respect to every varibles. We obtain a nontrivial solution by using the mountain pass lemma and an improved Lions lemma.