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Existence of a positive solution of an elliptic equation on RN

Published online by Cambridge University Press:  12 July 2007

Zhaoli Liu  and
Zhi-Qiang Wang
Zhaoli Liu
Affiliation:
Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA
Zhi-Qiang Wang
Affiliation:
Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USASchool of Mathematics and Computer Sciences, Fujian Normal University, Fuzhou 35007, People's Republic of China
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Abstract

We prove the existence of a positive solution for the Schrödinger-type equation on RN,−Δu + V(x)u = f(u) for u ∈ H1(RN), provided that The result is obtained in two cases. (a) lim|x|→ ∞V(x) = V (∞) ∈ (0,∞), f is subcritical and supt>0 2F(t)t−2 < V (∞). (b) There exist V > 0 and R* > 0 such that f(t)t−1 < V ∞ ≤ V (x) for all t > 0 and |x| ≥ R*.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 1 , February 2004 , pp. 191 - 200
Copyright
Copyright © Royal Society of Edinburgh 2004

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