Extremal solutions and Green's functions of higher order periodic boundary value problems in time scales

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:290

Article

Cabada, A

关键词: time scales;    lower and upper solutions;    monotone iterative technique;    Green functions;    maximum principles;   

DOI  :  10.1016/j.jmaa.2003.08.018

来源: Elsevier

【 摘 要 】

In this paper we develop the monotone method in the presence of lower and upper solutions for the problem [GRAPHICS] u(Delta i)(a)=u(Delta i)(sigma(b)), i=0,...,n-1 Here f:[a,b] x R-->R is such that f (., x) is rd-continuous in I for every x is an element of R and f (t, .) is continuous in R uniformly at t is an element of I, M-j is an element of R are given constants and [a,b]=T-kappa n for an arbitrary bounded time scale T. We obtain sufficient conditions in f to guarantee the existence and approximation of solutions lying between a pair of ordered lower and upper solutions alpha and beta. To this end, given M>0, we study some maximum principles related with operators [GRAPHICS] in the space of periodic functions. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

Free