Furtado, Marcelode Marchi, Reinaldo2022-03-162022-03-162017-01-13Furtado, M. F., & Marchi, R. (2017). Existence of solutions to asymptotically periodic Schrödinger equations. <i>Electronic Journal of Differential Equations, 2017</i>(15), pp. 1-7.1072-6691https://hdl.handle.net/10877/15520We show the existence of a nonzero solution for the semilinear Schrödinger equation -∆u + V(x)u = ƒ(x, u). The potential V is periodic and 0 belongs to a gap of σ(-∆ + V). The function ƒ is superlinear and asymptotically periodic with respect to x variable. In the proof we apply a new critical point theorem for strongly indefinite functionals proved in [3].Text7 pages1 file (.pdf)enAttribution 4.0 InternationalStrongly indefinite functionalsSchrödinger equationAsymptotically periodic problemArticle