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Open Access Open Badges Research Article

Eigenvalues of complementary Lidstone boundary value problems

Ravi P Agarwal12* and Patricia JY Wong3

Author Affiliations

1 Department of Mathematics, Texas A&M University - Kingsville, Kingsville, TX 78363, USA

2 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

3 School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

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Boundary Value Problems 2012, 2012:49  doi:10.1186/1687-2770-2012-49

Published: 24 April 2012


We consider the following complementary Lidstone boundary value problem

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/49/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/49/mathml/M1">View MathML</a>

where λ > 0. The values of λ are characterized so that the boundary value problem has a positive solution. Moreover, we derive explicit intervals of λ such that for any λ in the interval, the existence of a positive solution of the boundary value problem is guaranteed. Some examples are also included to illustrate the results obtained. Note that the nonlinear term F depends on y' and this derivative dependence is seldom investigated in the literature.

AMS Subject Classification: 34B15.

eigenvalues; positive solutions; complementary Lidstone boundary value problems