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Open AccessReview

A Review on a Class of Second Order Nonlinear Singular BVPs

Department of Mathematics, Indian Institute of Technology Patna, Patna 801106, Bihar, India
Department of Applied Sciences, Netaji Subhas Institute of Technology, Patna 801116, Bihar, India
Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA
Author to whom correspondence should be addressed.
Amit K. Verma dedicates this review to supervisor Prof. Rajni Kant Pandey, IIT Kharagpur.
Mathematics 2020, 8(7), 1045;
Received: 7 May 2020 / Revised: 20 June 2020 / Accepted: 22 June 2020 / Published: 28 June 2020
(This article belongs to the Special Issue Modelling and Analysis in Biomathematics)
Several real-life problems are modeled by nonlinear singular differential equations. In this article, we study a class of nonlinear singular differential equations, explore its various aspects, and provide a detailed literature survey. Nonlinear singular differential equations are not easy to solve and their exact solution does not exist in most cases. Since the exact solution does not exist, it is natural to look for the existence of the analytical solution and numerical solution. In this survey, we focus on both aspects of nonlinear singular boundary value problems (SBVPs) and cover different analytical and numerical techniques which are developed to deal with a class of nonlinear singular differential equations ( p ( x ) y ( x ) ) = q ( x ) f ( x , y , p y ) for x ( 0 , b ) , subject to suitable initial and boundary conditions. The monotone iterative technique has also been briefed as it gained a lot of attention during the last two decades and it has been merged with most of the other existing techniques. A list of SBVPs is also provided which will be of great help to researchers working in this area.
Keywords: review; nonlinear; singular; boundary value problems; Lane–Emden; Sturm–Liouville review; nonlinear; singular; boundary value problems; Lane–Emden; Sturm–Liouville
MDPI and ACS Style

Verma, A.K.; Pandit, B.; Verma, L.; Agarwal, R.P. A Review on a Class of Second Order Nonlinear Singular BVPs. Mathematics 2020, 8, 1045.

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