Triple solutions of complementary Lidstone boundary value problems via fixed point theorems
Wong, Patricia J. Y.
Date of Issue2014
School of Electrical and Electronic Engineering
We consider the following complementary Lidstone boundary value problem: (−1) m y (2m+1) (t)=F(t,y(t),y ′ (t)),t∈[0,1], y(0)=0,y (2k−1) (0)=y (2k−1) (1)=0,1≤k≤m. By using fixed point theorems of Leggett-Williams and Avery, we offer several criteria for the existence of three positive solutions of the boundary value problem. Examples are also included to illustrate the results obtained. We note that the nonlinear term F depends on y ′ and this derivative dependence is seldom investigated in the literature and a new technique is required to tackle the problem.
DRNTU::Engineering::Electrical and electronic engineering
Boundary value problems
© 2014 Wong; licensee Springer. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.