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Extremal solutions and Green's functions of higher order periodic boundary value problems in time scales
- Source :
-
Journal of Mathematical Analysis & Applications . Feb2004, Vol. 290 Issue 1, p35. 20p. - Publication Year :
- 2004
-
Abstract
- In this paper we develop the monotone method in the presence of lower and upper solutions for the problem uΔn(t)+∑lower limit j=1, upper limit n−1 MjuΔj(t)=f<fen><cp type="lpar" STYLE="S">t,u(t)<cp type="rpar" STYLE="S"></fen>, t∈[a,b],uΔi(a)=uΔi<fen><cp type="lpar" STYLE="S">σ(b)<cp type="rpar" STYLE="S"></fen>, i=0,…,n−1. Here <f>f :[a,b]×R→R</f> is such that <f>f(· ,x)</f> is rd-continuous in <f>I</f> for every <f>x∈R</f> and <f>f(t,·)</f> is continuous in <f>R</f> uniformly at <f>t∈I</f>, <f>Mj∈R</f> are given constants and <f>[a,b]=Tκn</f> for an arbitrary bounded time scale <f>T</f>. We obtain sufficient conditions in <f>f</f> to guarantee the existence and approximation of solutions lying between a pair of ordered lower and upper solutions <f>α</f> and <f>β</f>. To this end, given <f>M>0</f>, we study some maximum principles related with operators Tn±[M]u(t)≡uΔn(t)+∑lower limit j=1, upper limit n−1 MjuΔj(t)±Mu(t), in the space of periodic functions. [Copyright &y& Elsevier]
- Subjects :
- *GREEN'S functions
*MONOTONIC functions
*PERIODIC functions
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 290
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 11960625
- Full Text :
- https://doi.org/10.1016/j.jmaa.2003.08.018