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The Equation f′′′ + ff′′ + g(f′) = 0 and the Associated Boundary Value Problems

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Abstract

We study the concave and convex solutions of the third order similarity differential equation f′′′ + ff′′ + g(f′) = 0, and especially the ones that satisfies the boundary conditions f(0) = a, f′(0) = b and f′(t) → λ as t → + ∞, where λ is a root of the function g. According to the sign of g between b and λ, we obtain results about existence, uniqueness and boundedness of solutions to this boundary value problem, that we denote by \({({\mathcal P}_{{\bf g};a,b,\lambda})}\). In this way, we pursue and complete the study done in 2008.

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  1. Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, 4 rue des frères Lumière, 68093, Mulhouse Cedex, France

    Bernard Brighi

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  1. Bernard Brighi
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Brighi, B. The Equation f′′′ + ff′′ + g(f′) = 0 and the Associated Boundary Value Problems. Results. Math. 61, 355–391 (2012). https://doi.org/10.1007/s00025-011-0122-0

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  • DOI: https://doi.org/10.1007/s00025-011-0122-0

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