A class of nonlinear third-order boundary value problem with integral condition at resonance

A Third Order Nonlocal Boundary Value Problem at Resonance

We consider the third-order nonlocal boundary value problem u ′′′ (t) = f (t, u(t)), a.e. in (0, 1), u(0) = 0, u ′ (ρ) = 0, u ′′ (1) = λ[u ′′ ], where 0 < ρ < 1, the nonlinear term f satisfies Carathéodory conditions with respect to L 1 [0, T ], λ[v] = 1 0 v(t) dΛ(t), and the functional λ satisfies the resonance condition λ[1] = 1. The existence of a solution is established via Mawhin's coincid...

Numerical Treatment of Nonlinear Third Order Boundary Value Problem

In this paper, the boundary value problems for nonlinear third order differential equations are treated. A generic approach based on nonpolynomial quintic spline is developed to solve such boundary value problem. We show that the approximate solutions of such problems obtained by the numerical algorithm developed using nonpolynomial quintic spline functions are better than those produced by oth...

Existence of Positive Solutions of a Nonlinear Second-order Boundary-value Problem with Integral Boundary Conditions

In this article we prove the existence of at least one positive solution for a three-point integral boundary-value problem for a second-order nonlinear differential equation. The existence result is obtained by using Schauder’s fixed point theorem. Therefore, we do not need local assumptions such as superlinearity or sublinearity of the involved nonlinear functions.

Numerical solution for boundary value problem of fractional order with approximate Integral and derivative

Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three...

Second-Order Boundary Value Problem with Integral Boundary Conditions