Schrödinger type equations with asymptotically linear nonlinearities
type: Item
instance of: scholarly article
title: Schrödinger type equations with asymptotically linear nonlinearities
zbMATH Open document ID: 1030.35067
author: Francois A. van Heerden
author: Zhi-Qiang Wang
published in: Differential and Integral Equations
publication date: 2003-11-17T00:00:00Z
review text: The authors consider existence of solutions for the following nonlinear Schrödinger type equation \[ -\Delta u+(\lambda g(x)+1)u=f(u)\quad \text{in } \mathbb R^n \] which satisfy \(u(x)\to 0\) as \(|x|\to \infty.\) The nonlinearity \(f\) is assumed to be asymptotically linear and \(g(x)\geq 0\) has a potential well. Using variational techniques the authors prove existence of a positive solution for \(\lambda\) large. Multiple pairs of solutions are obtained in the case \(f\) is odd. The limiting behavior of solutions as \(\lambda\to \infty\) is also considered.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 2004900
zbMATH Keywords: nonlinear Schrödinger type equation
zbMATH Keywords: positive solutions
zbMATH Keywords: multiple solutions
zbMATH Keywords: asymptotically linear problem
reviewed by: Lubomira Softova
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2004900