This paper investigates the analytical approximate solutions of singular fourth order four-point boundary value problems using reproducing kernel method (RKM). The solution obtained by using the method takes the form of a convergent series with easily computable components. However, the reproducing kernel method can not be used directly to solve singular fourth order four-point boundary value p...

Many boundary value problems (BVPs) or initial BVPs have non-smooth solutions, with jumps along lower-dimensional interfaces. The Explicit–Jump Immersed Interface Method (EJIIM) was developed following Li’s Fast Iterative IIM (FIIIM), recognizing that the foundation for the efficient solution of many such problems is a good solver for elliptic BVPs. EJIIM generalizes the class of problems for w...

Two classes of multi-point BVPs for first order impulsive functional differential equations with nonlinear boundary conditions are studied. Sufficient conditions for the existence of at least one solution to these BVPs are established, respectively. Our results generalize and improve the known ones. Some examples are presented to illustrate the main results. c ©2012 NGA. All rights reserved.

Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernstein Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to ...

This paper is concerned with the existence of monotone positive solution for the following third-order nonlocal boundary value problem u′′′ (t)+f (t, u (t) , u′ (t)) = 0, 0 < t < 1; u (0) = 0, au′ (0) − bu′′ (0) = α[u], cu′ (1) + du′′ (1) = β[u], where f ∈ C([0, 1] × R+ × R+, R+), α[u] = ∫ 1 0 u(t)dA(t) and β[u] = ∫ 1 0 u(t)dB(t) are linear functionals on C[0, 1] given by Riemann-Stieltjes inte...

Solving boundary value problems BVPs for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic-type equation,...

A class of singularly perturbed two point Boundary Value Problems (BVPs) of reaction-diffusion type for third order Ordinary Differential Equations (ODEs) with a small positive parameter (ε) multiplying the highest derivative and a discontinuous source term is considered. The BVP is reduced to a weakly coupled system consisting of one first order ordinary differential equation with a suitable i...

In this article, we study five non-homogeneous multi-point boundary-value problems (BVPs) of second order differential equations with the onedimensional p-Laplacian. These problems have a common equation (in different function domains) and different boundary conditions. We find conditions that guarantee the existence of at least three positive solutions. The results obtained generalize several ...