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Unbounded Solutions of Third-Order Infinite Interval Problems Relevant to the Laminar Mixing Layer
  • Minghe Pei,
  • Libo Wang,
  • Xuezhe Lv
Minghe Pei
Beihua University
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Libo Wang
Beihua University

Corresponding Author:[email protected]

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Xuezhe Lv
Beihua University
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Abstract

In this paper, firstly, we apply the shooting method together with the Bolzano’s theorem and the maximum principle to present the existence, uniqueness, and qualitative properties of solutions to nonlinear third-order two-point boundary value problems on the half-line. And then, by employing the matching method, the existence, uniqueness, and qualitative properties of solutions to nonlinear third-order three-point boundary value problems on the whole real line are obtained. Finally, as applications, we mainly present the existence, uniqueness, and qualitative properties of solutions of the Blasius equations $y’‘’+yy’‘=0$ with one of the following boundary conditions $$ y’(-\infty)=C,~ y(0)=0,~ y’(+\infty)=1~ \hbox{with}~ 0\leq C<1, $$ $$ y’(-\infty)=C,~ y’‘’(0)=0,~ y’(+\infty)=1~ \hbox{with}~0\leq C<1, $$ which arise from the laminar mixing layer between two parallel flows with different velocities.