Multiple positive solutions for functional dynamic equations on time scales

Authors:
Da-Bin Wang;Jian-Ping Sun;Wen Guan
Affiliations:
Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, People's Republic of China;Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, People's Republic of China;Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu, 730050, People's Republic of China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

In this paper, we study the following functional dynamic equation on time scales: {[@F(u^@D(t))]^@?+a(t)f(u(t),u(@m(t)))=0,t@?(0,T)"T,u(t)=@f(t),t@?[-r,0)"T,u(0)-B"0(u^@D(0))=0,u^@D(T)=0, where @F:R-R is an increasing homeomorphism and a positive homomorphism and @F(0)=0. By using the well-known Leggett-Williams fixed point theorem, existence criteria for multiple positive solutions are established. An example is also given to illustrate the main results.