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Open Access Research

Existence of positive solutions for variable exponent elliptic systems

Samira Ala1*, Ghasem Alizadeh Afrouzi2, Qihu Zhang3 and Asadollah Niknam4

Author affiliations

1 Department of Mathematics, Sciences and Research, Islamic Azad University (IAU) Tehran, Iran

2 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

3 Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou, Henan 450002, China

4 Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

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Citation and License

Boundary Value Problems 2012, 2012:37  doi:10.1186/1687-2770-2012-37

Published: 3 April 2012

Abstract

We consider the system of differential equations

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/37/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/37/mathml/M1">View MathML</a>

where Ω ⊂ ℝN is a bounded domain with C2 boundary ∂Ω, 1 < p(x) ∈C1 <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/37/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/37/mathml/M2">View MathML</a> is a function. <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/37/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/37/mathml/M3">View MathML</a> is called p(x)-Laplacian. We discuss the existence of positive solution via sub-super solutions without assuming sign conditions on f(0), h(0).

MSC: 35J60; 35B30; 35B40.

Keywords:
positive solutions; p(x)-Laplacian problems; sub-supersolution