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Multiplicity of positive and nodal solutions for nonlinear elliptic problems in RN

Published online by Cambridge University Press:  14 November 2011

Ziqing Xie
Ziqing Xie
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha 410081, P.R. China
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Abstract

We consider the following problem:

where

for x ∈ RN, f(x, t), ft (x, t) ∈ C(RN × R), and f (x, t) ≧ 0 for all x ∈ RN and t ∈ R+, f(x, t) is an odd function of t. We show that if the maximum of Q(x) is achieved at k different points of RN, then for μ large enough the above problem has at least k positive solutions and k nodal solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 5 , 1998 , pp. 1069 - 1097
Copyright
Copyright © Royal Society of Edinburgh 1998

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