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Partially dissipative periodic processes

Jan Andres, Lech Górniewicz, Marta Lewicka (1996)

Banach Center Publications

Further extension of the Levinson transformation theory is performed for partially dissipative periodic processes via the fixed point index. Thus, for example, the periodic problem for differential inclusions can be treated by means of the multivalued Poincaré translation operator. In a certain case, the well-known Ważewski principle can also be generalized in this way, because no transversality is required on the boundary.

Positive periodic solutions of a neutral functional differential equation with multiple delays

Yongxiang Li, Ailan Liu (2018)

Mathematica Bohemica

This paper deals with the existence of positive ω -periodic solutions for the neutral functional differential equation with multiple delays ( u ( t ) - c u ( t - δ ) ) ' + a ( t ) u ( t ) = f ( t , u ( t - τ 1 ) , , u ( t - τ n ) ) . The essential inequality conditions on the existence of positive periodic solutions are obtained. These inequality conditions concern with the relations of c and the coefficient function a ( t ) , and the nonlinearity f ( t , x 1 , , x n ) . Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.

Positive periodic solutions of parabolic evolution problems: a translation along trajectories approach

Aleksander Ćwiszewski (2011)

Open Mathematics

A translation along trajectories approach together with averaging procedure and topological degree are used to derive effective criteria for existence of periodic solutions for nonautonomous evolution equations with periodic perturbations. It is shown that a topologically nontrivial zero of the averaged right hand side is a source of periodic solutions for the equations with increased frequencies. Our setting involves equations on closed convex cones, therefore it enables us to study positive solutions...

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