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On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions

Wenjie Gao, Junyu Wang (1995)

Annales Polonici Mathematici

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].

On boundary value problems of second order differential inclusions

Bapur Chandra Dhage (2004)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper presents sufficient conditions for the existence of solutions to boundary-value problems of second order multi-valued differential inclusions. The existence of extremal solutions is also obtained under certain monotonicity conditions.

On BVPs in l∞(A).

Gerd Herzog, Roland Lemmert (2005)

Extracta Mathematicae

We prove the existence of extremal solutions of Dirichlet boundary value problems for u''a + fa(t,u,u'a) = 0 in l∞(A) between a generalized pair of upper and lower functions with respect to the coordinatewise ordering, and for f quasimonotone increasing in its second variable.

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