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Open Access Research

Positive solutions for a class of sublinear elliptic systems

Ruyun Ma*, Ruipeng Chen and Yanqiong Lu

Author Affiliations

Department of Mathematics, Northwest Normal University, Lanzhou, 730070, PR China

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Boundary Value Problems 2014, 2014:28  doi:10.1186/1687-2770-2014-28

Published: 30 January 2014

Abstract

In this paper, we are concerned with the existence of positive solutions of the semilinear elliptic system

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/28/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/28/mathml/M1">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/28/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/28/mathml/M2">View MathML</a> is a parameter, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/28/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/28/mathml/M3">View MathML</a> is a continuous real function for each <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/28/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/28/mathml/M4">View MathML</a>. Under some appropriate assumptions, we show that the above system has at least one positive solution in certain interval of λ. The proofs of our main results are based upon bifurcation theory.

MSC: 34B15, 34B18.

Keywords:
sublinear elliptic systems; positive solutions; eigenvalues; bifurcation theory