TY - JOUR T1 - A Note on Existence of a Bound State for a Non-Autonomous Nonlinear Scalar Field Equation AU - Maia , Liliane A. AU - Moura , Elson L. JO - Analysis in Theory and Applications VL - 4 SP - 355 EP - 376 PY - 2020 DA - 2020/01 SN - 35 DO - http://doi.org/10.4208/ata.OA-0014 UR - https://global-sci.org/intro/article_detail/ata/13617.html KW - Schrödinger equation, asymptotically linear, superlinear, variational methods. AB -

The aim of this paper is to present a positive solution of a semilinear elliptic equation in $\mathbb{R}^{N}$ with non-autonomous non-linearities which are not necessarily pure-powers, nor homogeneous, and which are superlinear or asymptotically linear at infinity. The proof is variational combined with topological arguments.