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arXiv · 1508.07408

Nonlinear three point Singular BVPs : A Classification

Mandeep Singh·Amit K. Verma
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Abstract

We analyze the existence of unique solutions of the following class of nonlinear three point singular boundary value problems (SBVPs), \begin{eqnarray*}\label{NL-Singular-P} &&-(x^α y'(x))'= x^αf(x,y),\quad 0 0$, $0<η<1$ and $α\geq 1$. This study shows some novel observations regarding the nature of the solution of the nonlinear three point SBVPs. We observe that when $sup\left(\partial f/\partial y\right)>0$ for $α\in \cup_{n\in \mathbb{N}}\left(4n-1,4n+1\right)$ or $α\in\{1,5,9,\cdots\}$ reverse ordered case occur. When $sup\left(\partial f/\partial y\right)>0$ for $α\in \cup_{n\in \mathbb{N}}\left(4n-3,4n-1\right)$ or $α\in\{3,7,11,\cdots\}$ and when $sup\left(\partial f/\partial y\right)<0$ for all $α\geq 1$ well order case occur.

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Mandeep Singh, Amit K. Verma. 2017-03-26. Nonlinear three point Singular BVPs : A Classification. https://arxiv.org/abs/1508.07408

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