A nonlocal boundary value problem with singularities in phase variables

The singular differential equation (g(x'))' = f(t,x,x') together with the nonlocal boundary conditions x(0) = x(T) = -gamma min{x(t) : t is an element of [0,T]} is considered. Here g is an element of C-0(R) is an increasing and odd function, positive f satisfying the local Caratheodory conditions on [0, T] x (R \ {0})(2) may be singular at the value 0 in all its phase variables and gamma is an element of (0, infinity). The existence result for the above boundary value problem is proved by the regularization and sequential techniques. Proofs use the topological transversality principle and the Vitali's convergent theorem. (C) 2004 Elsevier Ltd. All rights reserved.