Article

# Solvability of a second-order multi-point boundary value problem at resonance.

School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, Jiangsu 221116, People’s Republic of China

Applied Mathematics and Computation (Impact Factor: 1.6). 02/2009; 208:23-30. DOI: 10.1016/j.amc.2008.11.026 Source: DBLP

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**ABSTRACT:**Sufficient conditions for the existence of solutions of a multi-point boundary value problem for an n-th order ordinary differential equation with a general right-hand side are given. The authors focus on the case when dimkerL=2, where L is related to the linear equation Lx:=x (n) (t)=0. Mawhin’s coincidence degree theory is applied for this aim. An illustrative example for a concrete third-order equation is supplied.Applications of Mathematics 01/2011; 6(6). · 0.15 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We obtain the expression of the explicit solution to a class of multipoint boundary value problems of Neumann type for linear ordinary differential equations and apply these results to study sufficient conditions for the existence of solution to linear functional differential equations with multipoint boundary conditions, considering the particular cases of equations with delay and integro-differential equations.Nonlinear Analysis Real World Applications 08/2012; 13(4):1662–1675. · 2.34 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In the previous works, the authors developed the reproducing kernel method (RKM) for nonlocal boundary value problems. A key of the method is the construction of the reproducing kernel (RK) satisfying the homogenous boundary conditions (BCs) of the considered problems. However, it is very difficult to obtain the RK of a reproducing kernel space satisfying nonlocal BCs or nonlinear BCs. Even if the RK is found, its representation is also very complicated compared with the RK without any BCs. In this paper, we will present a new RKM for linear nonlocal boundary value problems. The method can avoid reducing the inhomogeneous BCs to homogeneous BCs and constructing RK satisfying homogeneous nonlocal linear BCs. Numerical examples are provided to show the effectiveness of the new method.Applied Mathematics and Computation 12/2014; 248. · 1.35 Impact Factor

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