SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Open Badges 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

For all author emails, please log on.

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

Published: 15 May 2013


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.

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