In this paper, we study mixed boundary value problem for secondorder impulsive differential equations with a parameter. By using critical point theory, several new existence results are obtained. This is one of the first times that impulsive boundary value problems are studied by means of variational methods.

In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential equations of order q 2 (2; 3]. The Kras-noselskii's xed point theorem is applied to establish the results. In addition,we give an detailed example to demonstrate the main result.

In this paper, we prove the existence of the solution for boundary value prob-lem(BVP) of fractional dierential equations of order q 2 (2; 3]. The Kras-noselskii's xed point theorem is applied to establish the results. In addition,we give an detailed example to demonstrate the main result.

quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. convergence analysis of sixth order method has been given. the methods are illustrated by some examples, to verify the or...

IT is intuitively obvious that if a simple continuous curve is given in the (x, 2/)-plane, and a continuous distribution of values along the curve, there will exist functions of x and y which are continuous in both variables together, and which take on the prescribed values along the curve. It is the purpose of the present note to give an analytic proof of this fact, by elementary means, and, i...

We consider the boundary value problem:    x (m) (t) = f (t, x(t)), a ≤ t ≤ b, m > 1 x(a) = β 0 ∆x (k) ≡ x (k) (b) − x (k) (a) = β k+1 , continuous at least in the interior of the domain of interest. We give a constructive proof of the existence and uniqueness of the solution, under certain conditions, by Picard's iteration. Moreover Newton's iteration method is considered for the numerical ...

To solve numerically boundary value problems for parabolic equations with mixed derivatives, the construction of difference schemes with prescribed quality faces essential difficulties. In parabolic problems, some possibilities are associated with the transition to a new formulation of the problem, where the fluxes (derivatives with respect to a spatial direction) are treated as unknown quantit...

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

In this paper, we firstly obtain the existence of the monotone positive solutions and establish a corresponding iterative scheme for the following mixed-order four-point boundary value problem with p-Laplacian (φp(D α 0+u(t))) ′ + a(t)f(t, u(t), u′(t)) = 0, 0 < t < 1, u′(0)− βu(ξ) = 0, u′′(0) = 0, u′(1) + γu(η) = 0. Unlike many other fractional boundary value problem with p-Laplacian, the nonli...