Existence of solutions to the third-order nonlinear differential equations arising in boundary layer theory

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Abstract

By a new approach, we prove in this paper that there exists λ0 ϵ (−12, 0) such that the following third-order nonlinear boundary value problem for f(η): f‴+ff″+λ(1−f′2)=0, 0<η<∞,f(0)=0, f′(0)=0, f′(+∞)=1, which arises in boundary layer theory in fluid mechanics, has a solution at least for any fixed λ ϵ (λ0, 0).

Keywords

Singular boundary problems
Positive solutions
Fixed points

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I am grateful to Editor-in-Chief Prof Ervin Y. Rodin for his help and the referee for his careful reading and valuable suggestions.