A positive solution for a nonlinear schrödinger equation on ℝN

Louis Jeanjean; Kazunaga Tanaka

doi:10.1512/iumj.2005.54.2502

A positive solution for a nonlinear schrödinger equation on ℝ^N

Louis Jeanjean^*, Kazunaga Tanaka

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

138 Citations (Scopus)

Abstract

We prove the existence of a positive solution for a class of equations of the form -Δu + V(x)u = f(u), u ε H¹ (ℝ^N). On the nonlinearity f, only conditions around 0 and at ∞ are required.

Original language	English
Pages (from-to)	443-464
Number of pages	22
Journal	Indiana University Mathematics Journal
Volume	54
Issue number	2
DOIs	https://doi.org/10.1512/iumj.2005.54.2502
Publication status	Published - 2005

Keywords

Bounded ps sequences
Nonlinear elliptic equations
Variational methods

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1512/iumj.2005.54.2502

Cite this

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title = "A positive solution for a nonlinear schr{\"o}dinger equation on ℝN",

abstract = "We prove the existence of a positive solution for a class of equations of the form -Δu + V(x)u = f(u), u ε H1 (ℝN). On the nonlinearity f, only conditions around 0 and at ∞ are required.",

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KW - Nonlinear elliptic equations

KW - Variational methods

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