Positive solutions of complementary Lidstone boundary value problems

Abstract

We consider the following complementary Lidstone boundary value problem $$\begin{array}{c}(-1)^{m}y^{(2m+1)}(t)= F(t,y(t), y'(t)),~~t\in[0,1]\\ y(0)=0, y^{(2k-1)}(0)=y^{(2k-1)}(1)=0, 1\leq k\leq m. \end{array}$$ The nonlinear term $F$ depends on $y'$ and this derivative dependence is seldom investigated in the literature. Using a variety of fixed point theorems, we establish the existence of one or more positive solutions for the boundary value problem. Examples are also included to illustrate the results obtained.

Keywords

• derivative dependence
• positive solutions
• complementary lidstone boundary value problems