Alberto Cabada, "The method of lower and upper solutions for th-order periodic boundary value problems", International Journal of Stochastic Analysis, vol. 7, Article ID 737583, 15 pages, 1994. https://doi.org/10.1155/S1048953394000043
The method of lower and upper solutions for th-order periodic boundary value problems
In this paper we develop the monotone method in the presence of lower and upper solutions for the problem where is a Carathéodory function. We obtain sufficient conditions for to guarantee the existence and approximation of solutions between a lower solution and an upper solution for with either or .For this, we study some maximum principles for the operator . Furthermore, we obtain a generalization of the method of mixed monotonicity considering and as vectorial functions.
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