By means of the shooting method together with the maximum principle andthe Kneser–Hukahara continuum theorem, the authors present the existence, uniqueness and qualitative properties of solutions to nonlinear second-order boundary valueproblem on the semi-infinite interval of the following type:(y00 = f(x, y, y0), x ∈ [0, ∞),y0(0) = A, y(∞) = Band(y00 = f(x, y, y0), x ∈ [0, ∞),y(0) = A, y(∞) = B,where A, B ∈ R, f(x, y, z) is continuous on [0, ∞) × R2. These results and the matchingmethod are then applied to the search of solutions to the nonlinear second-order nonautonomous boundary value problem on the real line(y00 = f(x, y, y0), x ∈ R,y(?∞) = A, y(∞) = B,where A 6= B, f(x, y, z) is continuous on R3. Moreover, some examples are given toillustrate the main results, in which a problem arising in the unsteady flow of powerlaw fluids is included.
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