A singular boundary value problem for odd-order differential equations

Abstract

The odd-order differential equation (−1) n x (2 n+1) = f( t, x,…, x (2 n) ) together with the Lidstone boundary conditions x (2 j) (0)= x (2 j) ( T)=0, 0⩽ j⩽ n−1, and the next condition x (2 n) (0)=0 is discussed. Here f satisfying the local Carathéodory conditions can have singularities at the value zero of all its phase variables. Existence result for the above problem is proved by the general existence principle for singular boundary value problems.