Based on new information concerning strongly indefinite functionals without Palais–Smale conditions, we study existence and multiplicity of solutions of the Schrödinger equationwhere V and g are periodic with respect to x and 0 lies in a gap of σ(-Δ+V). Supposing g is asymptotically linear as |u|→∞ and symmetric in u, we obtain infinitely many geometrically distinct solutions. We also consider the situation where g is super linear with mild assumptions different from those studied previously, and establish the existence and multiplicity.
關聯:
Journal of Differential Equations, 222(1): 137-163
