EXISTENCE RESULTS FOR OPERATOR EQUATIONS INVOLVING DUALITY MAPPINGS VIA THE MOUNTAIN PASS THEOREM

摘要

We derive existence results for operator equations having the formrnJ_φu = N_fu, by using the Mountain Pass Theorem. Here J_φ is a duality mapping on a real reflexive and smooth Banach space, compactly imbedded in a L~q-space, and N_f is the Nemytskii operator generated by a Caratheodory function f which satisfies some appropriate growth conditions.