The method of lower and upper solutions for n th-order periodic boundary value problems. (1994)

• Record Type: Journal Article
• Authors: Cabada, Alberto
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 7:Number 1(1994)
• Page Start: 33
• Page End: 47
• Publication Date: 1994
• Subjects: periodic boundary value problem -- lower and upper solutions -- monotone method; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953394000043
• Languages: English
• ISSNs: 1048-9533

Abstract

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.