Abstract
ABSTRACT In this paper, we are concerned with the existence, multiplicity and concentration of positive solutions for the semilinear Schrödinger-Poisson system where (small) and λ are real parameters, a,b and c are continuous functions, and f is a continuous superlinear and subcritical nonlinearity. First, we prove that there are two families of semiclassical positive solutions for small. Then we show that these solutions are concentrating on some sets which is generated by the minimal points of a and maximal points of b and c. In addition, we investigate the relation between the number of positive solutions and the topology of the set of the global minima(or maxima) of the potentials by minimax theorems and the Ljusternik-Schnirelmann theory. Finally, we obtain some sufficient conditions for the nonexistence of positive ground state solutions.
Published Version
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