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ISSN 1449-5910  


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8: Paper Source PDF document

Paper's Title:

Equilibria and Periodic Solutions of Projected Dynamical Systems on Sets with Corners


Matthew D. Johnston and Monica-Gabriela Cojocaru

Department of Applied Mathematics, University of Waterloo,
Ontario, Canada

Department of Mathematics & Statistics, University of Guelph,
Ontario, Canada


Projected dynamical systems theory represents a bridge between the static worlds of variational inequalities and equilibrium problems, and the dynamic world of ordinary differential equations. A projected dynamical system (PDS) is given by the flow of a projected differential equation, an ordinary differential equation whose trajectories are restricted to a constraint set K. Projected differential equations are defined by discontinuous vector fields and so standard differential equations theory cannot apply. The formal study of PDS began in the 90's, although some results existed in the literature since the 70's. In this paper we present a novel result regarding existence of equilibria and periodic cycles of a finite dimensional PDS on constraint sets K, whose points satisfy a corner condition. The novelty is due to proving existence of boundary equilibria without using a variational inequality approach or monotonicity type conditions.

1: Paper Source PDF document

Paper's Title:

Local and Global Existence and Uniqueness Results for Second and Higher Order Impulsive Functional Differential Equations with Infinite Delay


Johnny Henderson and Abdelghani Ouahab

Department of Mathematics, Baylor University,
Waco, Texas 76798-7328

Laboratoire de Mathématiques, Université de Sidi Bel Abbés
BP 89, 22000 Sidi Bel Abbées,


In this paper, we discuss the local and global existence and uniqueness results for second and higher order impulsive functional differential equations with infinite delay. We shall rely on a nonlinear alternative of Leray-Schauder. For the global existence and uniqueness we apply a recent Frigon and Granas nonlinear alternative of Leray-Schauder type in Fréchet spaces.

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