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On meromorphic solutions of the Riccati differential equations

Ran Ran Zhang, Zong Xuan Chen (2010)

Annales Polonici Mathematici

We investigate the growth and Borel exceptional values of meromorphic solutions of the Riccati differential equation w' = a(z) + b(z)w + w², where a(z) and b(z) are meromorphic functions. In particular, we correct a result of E. Hille [Ordinary Differential Equations in the Complex Domain, 1976] and get a precise estimate on the growth order of the transcendental meromorphic solution w(z); and if at least one of a(z) and b(z) is non-constant, then we show that w(z)...

On noncompact perturbation of nonconvex sweeping process

Myelkebir Aitalioubrahim (2012)

Commentationes Mathematicae Universitatis Carolinae

We prove a theorem on the existence of solutions of a first order functional differential inclusion governed by a class of nonconvex sweeping process with a noncompact perturbation.

On nonlinear, nonconvex evolution inclusions

Nikolaos S. Papageorgiou (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, G δ -subset of the solution set of the original Cauchy problem. As an application, we obtain “bang-bang”’ type theorems for two nonlinear parabolic distributed parameter control systems.

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