Concentration and compactness in nonlinear Schrödinger-Poisson system with a general nonlinearity. (English) Zbl 1197.35096
Summary: We use a concentration and compactness argument to prove the existence of a nontrivial non-radial solution to the nonlinear Schrödinger-Poisson equations in \(\mathbb R^3\), assuming on the nonlinearity the general hypotheses introduced by Berestycki and Lions.
MSC:
| 35J47 | Second-order elliptic systems |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 47N20 | Applications of operator theory to differential and integral equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
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