Existence of Solution and Positive Solution to a Class of Nonlinear Second-Order Boundary Value Problems

journal6 ›› 2007, Vol. 28 ›› Issue (3): 1-5.

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Existence of Solution and Positive Solution to a Class of Nonlinear Second-Order Boundary Value Problems

(Department of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210003,China)

Online:2007-05-25 Published:2012-08-27
About author:YAO Qing-liu(1946-),male,was born in Shanghai,professor,research area is applied differential equation.
Supported by:
The National Natural Science Foundation (10571085)

Abstract

Abstract: The nonlinear second-order two-point boundaryvalue problem u″(t)+p(t)u′(t)+f(t,u(t),u′(t))=0,u(0)=A,u(1)=B is considered.By converting the problem into Sturm-Liouville problems and applying Leray-Schauder fixed point theorem,several existence results of solution and positive solution are obtained.The existence results show that the existence of solution and positive solution depends upon the “height” of nonlinear on certain bounded set.Our work extends previous results.

Key words: nonlinear ordinary differential equation, Sturm-Liouville problem, solution and positive solution, existence

YAO Qing-Liu. Existence of Solution and Positive Solution to a Class of Nonlinear Second-Order Boundary Value Problems[J]. journal6, 2007, 28(3): 1-5.

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Existence of Solution and Positive Solution to a Class of Nonlinear Second-Order Boundary Value Problems

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