Displaying similar documents to “Uniqueness for a class of cooperative systems of ordinary differential equations”

On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions

Wenjie Gao, Junyu Wang (1995)

Annales Polonici Mathematici

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The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].

Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions

Ming-Xing Wang, Alberto Cabada, Juan J. Nieto (1993)

Annales Polonici Mathematici

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The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.

On a Theorem of Mierczyński

Gerd Herzog (1998)

Colloquium Mathematicae

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We prove that the initial value problem x’(t) = f(t,x(t)), x ( 0 ) = x 1 is uniquely solvable in certain ordered Banach spaces if f is quasimonotone increasing with respect to x and f satisfies a one-sided Lipschitz condition with respect to a certain convex functional.