A note on nonautonomous Schrödinger equations with inhomogeneous nonlinearities - Lehrer, Raquel; Maia, Liliane; Ruviaro, Ricardo (Topological Methods in Nonlinear Analysis, 2024)
We study the existence of positive ground or bound state solutions for a class of nonlinear Schrödinger equations: equation*P_a -Δ u+λ u=a(x)f(u), u H^1(R^N), N ≥ 3, equation* where the function a is positive, symmetric under some group action G, and λ is a positive constant. The inhomogeneous nonlinearity f, under very mild assumptions, is asymptotically linear or superlinear and subcritical at infinity, with f(s)/s, s> 0, not satisfying any monotonicity condition.