Open Access Research

Multiple positive solutions for semilinear elliptic systems involving subcritical nonlinearities in R N

Huei-li Lin

Author Affiliations

Department of Natural Sciences in the Center for General Education, Chang Gung University, Tao-Yuan, 333, Taiwan, R.O.C

Boundary Value Problems 2012, 2012:118  doi:10.1186/1687-2770-2012-118

Published: 24 October 2012

Abstract

In this paper, we investigate the effect of the coefficient <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M2">View MathML</a> of the subcritical nonlinearity. Under some assumptions, for sufficiently small <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M3">View MathML</a>, there are at least k (≥1) positive solutions of the semilinear elliptic systems

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M4">View MathML</a>

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M5">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M6','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M6">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M7">View MathML</a> for <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/118/mathml/M8">View MathML</a>.

MSC: 35J20, 35J25, 35J65.

Keywords:
semilinear elliptic systems; subcritical exponents; Nehari manifold