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Representation of the set of mild solutions to the relaxed semilinear differential inclusion

Irene Benedetti, Elena Panasenko (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.

Response of a class of mechanical oscillators described by a novel system of differential-algebraic equations

Josef Málek, Kumbakonam R. Rajagopal, Petra Suková (2016)

Applications of Mathematics

We study the vibration of lumped parameter systems whose constituents are described through novel constitutive relations, namely implicit relations between the forces acting on the system and appropriate kinematical variables such as the displacement and velocity of the constituent. In the classical approach constitutive expressions are provided for the force in terms of appropriate kinematical variables, which when substituted into the balance of linear momentum leads to a single governing ordinary...

Réversibilité et classification des centres nilpotents

Michel Berthier, Robert Moussu (1994)

Annales de l'institut Fourier

Nous considérons un germe ω de 1-forme analytique dans 2 , 0 dont le 1-jet est y d y . Nous montrons que si l’équation ω = 0 définit un centre (i.e toutes les courbes solutions sont des cycles) il existe une involution analytique de 2 , 0 préservant le portrait de phase du système. Géométriquement ceci signifie que les centres analytiques nilpotents sont obtenus par image réciproque par des applications pli. Un théorème de conjugaison équivariante permet d’obtenir une classification complète de ces centres.

Riccati equations.

Williams, Lloyd K. (1987)

International Journal of Mathematics and Mathematical Sciences

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