Geodesic
Existence of solutions and convergence results for dynamic initial value problems using lower and upper solutions
Electronic journal of differential equations, Tome 2009 (2009)
In this article, we study the existence of solutions to first order non-linear initial value problems within the field of "dynamic equations on time scales". We employ the method of upper and lower solutions and Schauder's fixed point theorem. We also provide sufficient conditions under which the upper and lower solutions converge uniformly to a solution. Some examples are given to illustrate the new results.
Classification : 34N05, 26E70
Keywords: existence of solutions, non-linear nabla equations, lower and upper solutions, zero approximations 
@article{EJDE_2009__2009__a170,
     author = {Zaidi,  Atiya H.},
     title = {Existence of solutions and convergence results for dynamic initial value problems using lower and upper solutions},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1188.34121},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a170/}
}
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%J Electronic journal of differential equations
%D 2009
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Zaidi,  Atiya H. Existence of solutions and convergence results for dynamic initial value problems using lower and upper solutions. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a170/