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On the existence of multiple positive solutions to some superlinear systems

Published online by Cambridge University Press:  30 January 2012

M. Chhetri ,
S. Raynor  and
S. Robinson
M. Chhetri
Affiliation:
Department of Mathematics and Statistics, The University of North Carolina at Greensboro, NC 27402, USA (maya@uncg.edu)
S. Raynor
Affiliation:
Department of Mathematics, Wake Forest University, PO Box 7388, Winston Salem, NC 27109, USA (raynorsg@wfu.edu; sbr@wfu.edu)
S. Robinson
Affiliation:
Department of Mathematics, Wake Forest University, PO Box 7388, Winston Salem, NC 27109, USA (raynorsg@wfu.edu; sbr@wfu.edu)
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Abstract

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We use the method of upper and lower solutions combined with degree-theoretic techniques to prove the existence of multiple positive solutions to some superlinear elliptic systems of the form

on a smooth, bounded domain Ω⊂ℝn with Dirichlet boundary conditions, under suitable conditions on g1 and g2. Our techniques apply generally to subcritical, superlinear problems with a certain concave–convex shape to their nonlinearity.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 1 , February 2012 , pp. 39 - 59
Copyright
Copyright © Royal Society of Edinburgh 2012