Boundary value problems involving upper and lower solutions in reverse order

Authors:
Weibing Wang;Xuxin Yang;Jianhua Shen
Affiliations:
Department of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, PR China;Department of Mathematics, Hunan First Normal College, Changsha, Hunan 410205, PR China and Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, PR China;Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, we discuss the existence of extreme solutions of the boundary value problem for a class of first-order functional equations with a nonlinear boundary condition. In the presence of a lower solution @a and an upper solution @b with @b@?@a, we establish existence results of extreme solutions by using the method of upper and lower solutions and a monotone iterative technique.