A CLASS OF 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 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

Positive Solutions for Second-order Boundary Value Problem with Integral Boundary Conditions at Resonance on a Half-line

This paper deals with the second order boundary value problem with integral boundary conditions on a half-line: (p(t)x′(t))′ + g(t)f(t, x(t)) = 0, a.e. in (0,∞), x(0) = ∫ ∞ 0 x(s)g(s)ds, lim t→∞ p(t)x′(t) = p(0)x′(0). A new result on the existence of positive solutions is obtained. The interesting points are: firstly, the boundary value problem involved in the integral boundary condition on unb...

On a class of second-order impulsive boundary value problem at resonance

We consider the following impulsive boundary value problem, x′′(t) = f (t,x,x′), t ∈ J \ {t1, t2, . . . , tk}, x(ti)= Ii(x(ti),x′(ti)), x′(ti)= Ji(x(ti),x′(ti)), i= 1,2, . . . ,k, x(0)= 0, x′(1) = ∑m−2 j=1 αjx′(ηj). By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than r...