Existence and Multiplicity Results for Systems of Singular Boundary Value Problems

TL;DR

This paper investigates the existence of positive solutions for systems of singular boundary value problems in ordinary differential equations, using regularization and fixed point methods, with applications in physics and engineering.

Contribution

It provides new existence results for systems of SBVPs with unbounded nonlinearities, including singularities in variables and derivatives, based on regularization and sequential procedures.

Findings

Established existence of positive solutions for various SBVP systems.

Extended results to problems with singularities in variables and derivatives.

Utilized regularization and fixed point theory techniques.

Abstract

Singular boundary value problems (SBVPs) arise in various fields of Mathematics, Engineering and Physics such as boundary layer theory, gas dynamics, nuclear physics, nonlinear optics, etc. The present monograph is devoted to systems of SBVPs for ordinary differential equations (ODEs). It presents existence theory for a variety of problems having unbounded nonlinearities in regions where their solutions are searched for. The main focus is to establish the existence of positive solutions. The results are based on regularization and sequential procedure. First chapter of this monograph describe the motivation for the study of SBVPs. It also include some available results from functional analysis and fixed point theory. The following chapters contain results from author's PhD thesis, National University of Sciences and Technology, Islamabad, Pakistan. These results provide the existence of positive solutions for a variety of systems of SBVPs having singularity with respect to independent and/or dependent variables as well as with respect to the first derivatives of dependent variables.