Application of the shooting method to second-order multi-point integral boundary-value problems
School of Mathematics and Physics, University of South China, Hengyang, 421001, P.R. China
Boundary Value Problems 2013, 2013:205 doi:10.1186/1687-2770-2013-205Published: 9 September 2013
In this paper, we focus on the following second-order multi-point integral boundary-value problem:
where , for and are given constants. The proof is based on the shooting method. By constructing a quadratic function and a sine function as the shooting objects and combining the integral mean value theorem with the comparison principle, we consider the existence of positive solutions to the BVP respectively under the case and the case . The method is concise and some new criteria are established.
MSC: 34B10, 34B15, 34B18.