Nonlinear eigenvalue problems for higher order Lidstone boundary value problems

In this paper, we consider the Lidstone boundary value problem y (2m) (t) = a (t)f(y(t); : : : ; y (2j) (t); : : : y (2(m 1)) (t)), 0 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 xed point theorem. This in turn yields a interval on which there exists a nontrivial solution in a cone for each in that interval. The methods of the paper are known. The emphasis here is that f depends upon higher order derivatives. Appli- cations are made to problems that exhibit superlinear or sublinear type growth.