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: 1.35). 01/2009; 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). · 0.22 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We show that it is important to allow the nonlinear term to change sign when discussing existence of a positive solution for multipoint, or more general nonlocal, boundary value problems in the resonant case. When the nonlinear term has a fixed sign we obtain simple necessary and sufficient conditions for the existence of positive solutions.Applied Mathematics and Computation 03/2010; 216(2):497–500. · 1.35 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. · 2.20 Impact Factor

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