Existence of solution to first-order multipoint boundary value problems / Diana Sirmayunie Mohd Nasir (original) (raw)

Non-Linear First-Order Differential Boundary Problems with Multipoint and Integral Conditions

Fractal and Fractional, 2021

This paper considers boundary value problem (BVP) for nonlinear first-order differential problems with multipoint and integral boundary conditions. A suitable Green function was constructed for the first time in order to reduce this problem into a corresponding integral equation. So that by using the Banach contraction mapping principle (BCMP) and Schaefer’s fixed point theorem (SFPT) on the integral equation, we can show that the solution of the multipoint problem exists and it is unique.

Fixed Point Theory Approach to Existence of Solutions with Differential Equations

Differential Equations - Theory and Current Research

In this chapter, we introduce a generalized contractions and prove some fixed point theorems in generalized metric spaces by using the generalized contractions. Moreover, we will apply the fixed point theorems to show the existence and uniqueness of solution to the ordinary difference equation (ODE), Partial difference equation (PDEs) and fractional boundary value problem.

Existence and uniqueness of solutions for the first-order non-linear differential equations with three-point boundary conditions

Filomat

In this paper the existence and uniqueness of the solutions to boundary value problems for the first order non-linear system of the ordinary differential equations with three-point boundary conditions are investigated. For the first time the Green function is constructed and the considered problem is reduced to the equivalent integral equations that allow us to prove the existence and uniqueness theorems in differ from existing works, applying the Banach contraction mapping principle and Schaefer?s fixed point theorem. An example is given to illustrate the obtained results.

Existence of Solutions for Boundary Value Problems via F-Contraction Mappings in Metric Spaces

Nonlinear functional analysis and applications, 2020

The purpose of this paper is to present some sufficient conditions for the existence and uniqueness of solutions of the nonlinear Hammerstein integral equations and the two-point boundary value problems for nonlinear second-ordinary differential equations. To establish this, we introduce the generalized Suzuki-( α, β )- F -contraction and the generalized ( α, β )- F -contraction in the framework of a metric space and establish some fixed point results. The results obtained in this work provide extension as well as substantial generalization and improvement of several well-known results on fixed point theory and its applications.