Non-Linear First-Order Differential Boundary Problems with Multipoint and Integral Conditions
Mısır J. Mardanov, Yagub A. Sharifov, Yusif S. Gasimov, Carlo Cattani
Abstract
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.
Topics & Concepts
MathematicsBoundary value problemFixed-point theoremIntegral equationMathematical analysisContraction mappingContraction principleNonlinear systemOrder (exchange)PhysicsEconomicsFinanceQuantum mechanicsNonlinear Differential Equations AnalysisDifferential Equations and Boundary ProblemsDifferential Equations and Numerical Methods