Two-Point Boundary Value Problems for a Class of Second-Order Ordinary Differential Equations. (5th March 2012) - SenGupta, Indranil; Mariani, Maria C.
Abstract : We study the general semilinear second-order ODE u ′′ + g ( t, u, u ′ ) = 0 under different two-point boundary conditions. Using the method of upper and lower solutions, we obtain an existence result. Moreover, under a growth condition on g, we prove that the set of solutions of u ′′ + g ( t, u, u ′ ) = 0 is homeomorphic to the two-dimensional real space.