A DIMENSION-DEPENDING MULTIPLICITY RESULT FOR A PERTURBED SCHRODINGER EQUATION

We consider the Schrodinger equation[GRAPHICS],where N = 2, lambda,mu 0 are parameters, V, K, L : R-N - R are radially symmetric potentials, f : R - R is a continuous function with sublinear growth at infinity, and g : R - R is a continuous sub-critical function. We first prove that for lambda small enough no non-zero solution exists for (P-lambda,P-0), while for A large and . small enough at least two distinct non-zero radially symmetric solutions do exist for (P-lambda,P-mu). By exploiting a Ricceri-type three-critical points theorem, the principle of symmetric criticality and a group-theoretical approach, the existence of at least N - 3 (N mod 2) distinct pairs of non-zero solutions is guaranteed for (P-lambda,P-mu) whenever lambda is large and mu is small enough, N does not satisfy 3, and f,g are odd.