Positive solutions of nonlinear m-point BVP for an increasing homeomorphism and homomorphism with sign changing nonlinearity on time scales

Authors:
Yanbin Sang;Hua Su;Fuyi Xu
Affiliations:
Department of Mathematics, North University of China, Taiyuan, Shanxi, 030051, China;School of Statistics and Mathematics, Shandong University of Finance, Jinan, Shandong, 250014, China;School of Mathematics and Information Science, Shandong University of Technology, Zibo, Shandong, 255049, China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this paper, several existence theorems of positive solutions are established for nonlinear m-point boundary value problem for the following dynamic equations on time scales (@f(u^@D))^@?+a(t)f(t,u(t))=0,t@?[0,T],@f(u^@D(0))=@?i=1m-2a"i@f(u^@D(@x"i)),u(T)=@?i=1m-2b"iu(@x"i), where @f:R@?R is an increasing homeomorphism and homomorphism and @f(0)=0. The nonlinear term f may change sign. As an application, an example to demonstrate our results is given.