On a periodic Schrödinger equation involving periodic and nonperiodic nonlinearities in \(\mathbb{R}^2\)
This paper deals with a Schrödinger-type equation involving periodic and nonperiodic nonlinearities in the two-dimensional Euclidean space. The problem also contains a potential \(V\) that is 1-periodic and such that 0 lies in a spectral gap of the spectrum of the linear Schrödinger l operator \(-\Delta + V\). The reaction has exponential growth in the sense of Trudinger-Moser. The nonlinear term is allowed to be both periodic and nonperiodic in the spatial variable. The proofs combine the linking theorem and the Lions concentration-compactness principle.
scientific article; zbMATH DE number 6877120
scientific article