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Zbl 1056.39018
Extremal solutions and Green's functions of higher order periodic boundary value problems in time scales.
(English)
[J] J. Math. Anal. Appl. 290, No. 1, 35-54 (2004). ISSN 0022-247X

The author develops a monotone iterative method in the presence of lower and upper solutions for the problem $$u^{\Delta^n}(t)+\sum_{j=1}^{n-1}M_j u^{\Delta^j}(t)=f(t,u(t)), \quad t\in [a,b]=T^{\kappa^n}$$ $$u^{\Delta^i}(a)=u^{\Delta^i}(\sigma(b)), \quad i=0,1,\dots,n-1.$$ Sufficient conditions are obtained on $f$ to guarantee the existence and approximation of a solution lying between a pair of ordered lower and upper solutions.
[Patricia J. Y. Wong (Singapore)]
MSC 2000:
*39A12 Discrete version of topics in analysis
34B27 Green functions
93C70 Time-scale analysis and related topics
34B15 Nonlinear boundary value problems of ODE

Keywords: extremal solutions; Green's function; periodic boundary value problems; time scales; Lower and upper solutions; Monotone iterative technique; Maximum principles

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