Open Access Research

Positive solutions for classes of multi-parameter fourth-order impulsive differential equations with one-dimensional singular p-Laplacian

Xuemei Zhang1* and Meiqiang Feng2

Author Affiliations

1 Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206, Republic of China

2 School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, Republic of China

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Boundary Value Problems 2014, 2014:112  doi:10.1186/1687-2770-2014-112

Published: 13 May 2014

Abstract

The authors consider the following impulsive differential equations involving the one-dimensional singular p-Laplacian: <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M1">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M2">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M3">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M4">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M5">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M4">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M7','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M7">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M8','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M8">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M9','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M9">View MathML</a>, where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M10','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M10">View MathML</a> and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M11','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M11">View MathML</a> are two parameters. Several new and more general existence and multiplicity results are derived in terms of different values of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M12','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M12">View MathML</a> and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M11','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/112/mathml/M11">View MathML</a>. In this case, our results cover equations without impulsive effects and are compared with some recent results.

Keywords:
multi-parameter; impulsive differential equations; one-dimensional singular p-Laplacian; positive solution; cone and partial ordering