The Existence Of Two Nonnegative Solutions Of The Generalized Choquard-Pekar Equation

In this paper,we mainly study the existence of the solutions of the generalized Choquard-Pekar equation This kind of problem has strong physical meaning and certain application value.we use the concentration-compactness principle,the variational method and the locally minimal method to prove that under certain conditions there are at least two non-negative solutions to the above problem.One solution is obtained by locally minimal method,and the other solution is obtained by using the mountain pass lemma.