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

Aleksander Ćwiszewski

Open Mathematics (2011)

  • Volume: 9, Issue: 2, page 244-268
  • ISSN: 2391-5455

Abstract

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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 of nonlinear parabolic partial differential equations.

How to cite

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Aleksander Ćwiszewski. "Positive periodic solutions of parabolic evolution problems: a translation along trajectories approach." Open Mathematics 9.2 (2011): 244-268. <http://eudml.org/doc/269288>.

@article{AleksanderĆwiszewski2011,
abstract = {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 of nonlinear parabolic partial differential equations.},
author = {Aleksander Ćwiszewski},
journal = {Open Mathematics},
keywords = {Semigroup; Evolution equation; Topological degree; Periodic solution; semigroup; evolution equation; topological degree; periodic solution},
language = {eng},
number = {2},
pages = {244-268},
title = {Positive periodic solutions of parabolic evolution problems: a translation along trajectories approach},
url = {http://eudml.org/doc/269288},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Aleksander Ćwiszewski
TI - Positive periodic solutions of parabolic evolution problems: a translation along trajectories approach
JO - Open Mathematics
PY - 2011
VL - 9
IS - 2
SP - 244
EP - 268
AB - 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 of nonlinear parabolic partial differential equations.
LA - eng
KW - Semigroup; Evolution equation; Topological degree; Periodic solution; semigroup; evolution equation; topological degree; periodic solution
UR - http://eudml.org/doc/269288
ER -

References

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