EXISTENCE OF A NONTRIVIAL SOLUTION TO A STRONGLY INDEFINITE SEMILINEAR EQUATION

Under general hypotheses, we prove the existence of a nontrivial solution for the equation Lu = N(u) , where u belongs to a Hilbert space H, L is an invertible continuous selfadjoint operator, and N is superlinear. We are particularly interested in the case where L is strongly indefinite and N is not compact. We apply the result to the Choquard-Pekar equation [GRAPHICS] where p is-an-element-of L(infinity) R3 is a periodic function.