Topological degree methods in BVPS with nonlinear conditions - Rachůnková, Irena (Annales Mathematicae Silesianae, 1996)
We consider the second order differential equation x" = f(t,x,x'), where f is a Carathéodory function. We prove the existence of at least one solution of the equation satisfying the nonlinear boundary conditions g1(x(a),x'(a)) = 0, g2(x(b),x'(b)) = 0. Our methods of proofs are based on the topological degree arguments for auxiliary operator equation.