Positive solutions of complementary lidstone boundary value problems - Agarwal, Ravi P. (2014)
We consider the following complementary Lidstone boundary value problem (−1)my (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. 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.