Existence, uniqueness and qualitative properties of heteroclinic solutions to nonlinear second-order ordinary differential equations

Abstract

By means of the shooting method together with the maximum principle and the Kneser-Hukahara continuum theorem, the authors present the existence, uniqueness and qualitative properties of solutions to nonlinear second-order boundary value problem on the semi-infinite interval of the following type: {y" = f (x, y, y'), x is an element of [ 0, infinity), y'(0) = A, y (infinity) = B and (y" = f (x, y, y'), x is an element of [ 0, infinity), y(0) = A, y (infinity) = B, where A, B is an element of R, f (x, y, z) is continuous on [0, infinity) x R-2. These results and the matching method are then applied to the search of solutions to the nonlinear second-order non-autonomous boundary value problem on the real line {y" = f (x, y, y'), x is an element of R, y(-infinity) = A, y(infinity) = B, where A not equal B, f (x, y, z) is continuous on R-3. Moreover, some examples are given to illustrate the main results, in which a problem arising in the unsteady flow of power-law fluids is included.