In this paper, we study the existence of three solutions to the following nonlinear m-point boundary value problem  u′′(t) + βu(t) = h(t)f(t, u(t)), 0 < t < 1, u′(0) = 0, u(1) = m−2 ∑ i=1 αiu(ηi), where 0 < β < π2 , f ∈ C([0, 1] × R ,R). h(t) is allowed to be singular at t = 0 and t = 1. The arguments are based only upon the Leggett-Williams fixed point theorem. We also prove nonexist results.

A new comparison theorem is proved and then used to investigate the solvability of a third-order two-point boundary value problem  u′′′(t) + f(t, u(t), u′(t), u′′(t))) = 0, u(0) = u′(2π) = 0, u′′(0) = u′′(2π). Some existence results are established for this problem via upper and lower solutions method and fixed point theory. 2000MR Subject Classification: 34B15, 34C05

Abstract We study difference equations which arise as discrete approximations to three-point boundary value problems for systems of first-order ordinary differential equations. We obtain new results of the existence of solutions to the discrete problem by employing Euler’s method. The existence of solutions are proven by the contraction mapping theorem and the Brouwer fixed point theorem in Euc...

The optimal path planning of cooperative manipulators is studied in the present research. Optimal Control Theory is employed to calculate the optimal path of each joint choosing an appropriate index of the system to be minimized and taking the kinematics equations as the constraints. The formulation has been derived using Pontryagin Minimum Principle and results in a Two Point Boundary Value Pr...

In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.

This paper is concerned with a 2nth-order p-Laplacian difference equation. By using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for Neumann boundary value problem and give some new results. Results obtained successfully generalize and complement the existing ones.

‎in this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎by applying kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary bvp formulated by truncating the response function‎. ‎then the arzela--ascoli theorem is used to take $c^1$ ...

in this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

In this paper, a Chebyshev finite difference method has been proposed in order to solve nonlinear two-point boundary value problems for second order nonlinear differential equations. A problem arising from chemical reactor theory is then considered. The approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference schem...