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Existence of changing sign solutions for some semilinear problems with jumping nonlinearities at zero

Published online by Cambridge University Press:  14 November 2011

E. N. Dancer  and
Yihong Du
E. N. Dancer
Affiliation:
Department of Mathematics, Statistics and Computing Science, The University of New England, Armidale, NSW 2351, Australia
Yihong Du
Affiliation:
Department of Mathematics, Statistics and Computing Science, The University of New England, Armidale, NSW 2351, Australia
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Abstract

We study the existence of changing sign solutions of an elliptic semilinear boundary value problem, which arises as a limiting equation of the two species Lotka–Volterra competing equations system. Using variational methods and a result of D'Aujourd'hui, we find conditions which are both sufficient and necessary for this existence problem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 6 , 1994 , pp. 1165 - 1176
Copyright
Copyright © Royal Society of Edinburgh 1994

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