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:\begin{equation*}\label{P_a}-\Delta u+\lambda u=a(x)f(u), \quad u \in H^1\big(\mathbb{R}^N\big), \ N \geq 3,\end{equation*}where the function a is positive, symmetric under some group action $G$,and $\lambda$ 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.