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Existence and nonexistence of entire positive solutions for ( p , q ) -Laplacian elliptic system with a gradient term

Zhong Bo Fang1* and Su-Cheol Yi2

Author Affiliations

1 School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, P.R. China

2 Department of Mathematics, Changwon National University, Changwon, 641-773, Republic of Korea

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Boundary Value Problems 2013, 2013:18  doi:10.1186/1687-2770-2013-18

Published: 5 March 2013

Abstract

This work is concerned with the entire positive solutions for a <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/18/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/18/mathml/M1">View MathML</a>-Laplacian elliptic system of equations with a gradient term. We find the sufficient condition for nonexistence of entire large positive solutions and existence of infinitely many entire solutions, which are large or bounded.