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On a class of semilinear elliptic systems

Published online by Cambridge University Press:  14 November 2011

Yaping Liu
Yaping Liu
Affiliation:
Department of Mathematics, Kansas State University, Manhattan, Kansas 66506, U.S.A.
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Abstract

A class of semilinear elliptic systems of two equations is considered. Sufficient conditions are given for the existence of different types of sign-definite solutions. These conditions relate the larger eigenvalues of certain 2 × 2 real matrices associated with the system to the first eigenvalue of − ∆ under the homogeneous Dirichlet boundary condition. A special case provides a complementary result to some of the recent works.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 3 , 1994 , pp. 609 - 620
Copyright
Copyright © Royal Society of Edinburgh 1994

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