A note on nonautonomous Schrödinger equations with inhomogeneous nonlinearities
DOI:
https://doi.org/10.12775/TMNA.2024.021Keywords
Schrödinger, symmetric, positive solutionsAbstract
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.References
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