Differential equations with nonlocal boundary conditions

In this work, we investigate the existence of solutions of the differential equation -u" = f (t, u, u'), 0 < t < 1 with the nonlocal boundary conditions u (0) = c(o) + g(o) (u) and u (1) = c(1) + g(1) (u). Integral nonlocal conditions have been used in connection with thermal conduction problems, semiconductor problems, and problems in hydrodynamics. Several techniques can be used to handle this type of problems, for instance fixed point theory, topological transversality theory, the upper and lower solutions method.