Existence results are established for the equation y '' +f(t, y) = 0, 0 < t < 1. Here f may be singular in y and f is allowed to change sign. Our boundary data include y(0) = y'(1) + ky(1) = 0, k > -1 and y(0) = ...

The Schauder Tychonoff theorem in a locally convex topological space is used to establish existence results for Volterra-Hammmerstein and Hammerstein integral equations in a reflexive Banach space.

We prove the existence of nonnegative solutions of the problem (py')'/p + mu qg(x, y) = 0, lim(x-->0+)py' = 0, h(y'(1)) + y(1) = 0 for a physically motivated class of nonlinearity h. The results, which are established ...