American Institute of Mathematical Sciences

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July  2008, 7(4): 787-793. doi: 10.3934/cpaa.2008.7.787

Existence and multiplicity of solutions for a weakly coupled radial system in a ball

E. N. Dancer 1, and  Sanjiban Santra 2,

1. 

School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia
2. 

Department of Mathematics, Chinese University of Hong Kong

Received  May 2007 Revised  February 2008 Published  April 2008

We prove a conjecture by Dalbono-McKenna on the number of solutions for a weakly coupled elliptic system. The system is of the Ambrosetti-Prodi type with a asymmetric nonlinearity. We consider the radial case in a ball. By applying a degree theoretic argument, we simplify the proof of the paper [3] and obtain the existence and multiplicity of solutions for this weakly coupled system.
Keywords: bifurcation, degree theory., Weakly coupled system.
Mathematics Subject Classification: Primary: 35G25, 35G65; Secondary: 34B1.
Citation: E. N. Dancer, Sanjiban Santra. Existence and multiplicity of solutions for a weakly coupled radial system in a ball. Communications on Pure and Applied Analysis, 2008, 7 (4) : 787-793. doi: 10.3934/cpaa.2008.7.787
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