EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTION FOR NONLINEAR SINGULAR 2mth-ORDER CONTINUOUS AND DISCRETE LIDSTONE BOUNDARY VALUE PROBLEMS

• Published in: Acta mathematica scientia Vol. 31; no. 1; pp. 281 - 291
• Main Author: 苑成军 文香丹 蒋达清
• Format: Journal Article
• Language: English
• Published: School of Mathematics and Computer, Harbin University, Harbin 150086, China%Department of Mathematics, Yanbian University, Yanji 133002, China%School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China 2011; School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
• Subjects: Boundary value problems; Difference equations; Differential equations; Existence theorems; Mathematical analysis; Nonlinearity; Operators; Theorems; Uniqueness; 存在唯一性; 常微分方程; 正解的存在性; 混合单调算子; 边值问题; 非线性项; existence; uniqueness; Mixed monotone operator; boundary value problems; fixed point theorem
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(11)60228-2

By fixed point theorem of a mixed monotone operators, we study Lidstone boundary value problems to nonlinear singular 2mth-order differential and difference equations, and provide sufficient conditions for the existence and uniqueness of positive solution to Lidstone boundary value problem for 2mth-order ordinary differential equations and 2mth-order difference equations. The nonlinear term in the differential and difference equation may be singular.