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Open Access Research

On positive solutions to equations involving the one-dimensional p-Laplacian

Ruyun Ma*, Yanqiong Lu and Ahmed Omer Mohammed Abubaker

Author Affiliations

Department of Mathematics, Northwest Normal University, Lanzhou, 730070, P.R. China

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Boundary Value Problems 2013, 2013:125  doi:10.1186/1687-2770-2013-125

Published: 15 May 2013

Abstract

We consider equations involving the one-dimensional p-Laplacian

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/125/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/125/mathml/M1">View MathML</a>

with the Dirichlet boundary conditions. By using time map methods, we show how changes of the sign of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/125/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/125/mathml/M2">View MathML</a> lead to multiple positive solutions of the problem for sufficiently large λ.

MSC: 34B10, 34B18.

Keywords:
positive solutions; one-dimensional p-Laplacian; uniqueness; time map