Electronic Journal of Qualitative Theory of Differential Equations
In this paper, we consider the Lidstone boundary value problem y(t) = λa(t)f(y(t), . . . , y(t), . . . y(t)), 0 < t < 1, y(0) = 0 = y(1), i = 0, . . . , m − 1, where (−1)f > 0 and a is nonnegative. Growth conditions are imposed on f and inequalities involving an associated Green’s function are employed which enable us to apply a well-known cone theoretic fixed point theorem. This in turn yields a λ interval on which there exists a nontrivial solution in a cone for each λ in that interval. The methods of the paper are known. The emphasis here is that f depends upon higher order derivatives. Applications are made to problems that exhibit superlinear or sublinear type growth.
No. 2, 8
Eloe, Paul W., "Nonlinear eigenvalue problems for higher order Lidstone boundary value problems" (2000). Mathematics Faculty Publications. 103.