The method of lower and upper solutions for n th-order periodic boundary value problems

Alberto Cabada

International Journal of Stochastic Analysis, 1994, vol. 7, 1-15

Abstract:

In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u ( n ) ( t ) = f ( t , u ( t ) ) ; u ( i ) ( a ) − u ( i ) ( b ) = λ i ∈ ℝ , i = 0 , … , n − 1 where f is a Carathéodory function. We obtain sufficient conditions for f to guarantee the existence and approximation of solutions between a lower solution α and an upper solution β for n ≥ 3 with either α ≤ β or α ≥ β .

For this, we study some maximum principles for the operator L u ≡ u ( n ) + M u . Furthermore, we obtain a generalization of the method of mixed monotonicity considering f and u as vectorial functions.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:737583

DOI: 10.1155/S1048953394000043

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