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Existence and Uniqueness of a Non-Negative Monotonic Solution of a Nonlinear Ordinary Differential Equation

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Abstract

In this paper, we prove the existence and uniqueness of a non-negative monotonically increasing solution of the boundary value problem (BVP)

$$\begin{aligned}&H''(\eta )-H^p(\eta )H'(\eta )+\frac{\eta }{2}H'(\eta )+\frac{1}{2p}H(\eta )=0,\quad \eta >0,\\&H(0)=0,\quad \lim _{\eta \rightarrow +\infty }\eta ^{-\frac{1}{p}}H(\eta )=1, \end{aligned}$$

using a shooting argument for \(p>1\). This BVP arises when we construct the large time asymptotic solution of the modified Burgers equation, using the method of matched asymptotic expansions, on the quarter plane.

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Acknowledgements

We thank the referees for their valuable comments and suggestions which have improved the paper.

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  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India

    P. Samanta & Ch. Srinivasa Rao

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  1. P. Samanta
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Correspondence to Ch. Srinivasa Rao.

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Samanta, P., Rao, C.S. Existence and Uniqueness of a Non-Negative Monotonic Solution of a Nonlinear Ordinary Differential Equation. Differ Equ Dyn Syst 30, 957–968 (2022). https://doi.org/10.1007/s12591-019-00483-x

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