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

DOI10.2478/s11533-011-0010-6zbMath1222.47132OpenAlexW2019388163WikidataQ96744681 ScholiaQ96744681MaRDI QIDQ539204

Aleksander Ćwiszewski

Publication date: 27 May 2011

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-011-0010-6

zbMATH Keywords

evolution equationsemigroupperiodic solutiontopological degree

Mathematics Subject Classification ID

Degree theory for nonlinear operators (47H11) Abstract bifurcation theory involving nonlinear operators (47J15) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05) Nonlinear evolution equations (47J35)

Related Items

The Krasnosel'skii formula for parabolic differential inclusions with state constraints ⋮ Periodic \(\mathrm{L}_p\) estimates by \(\mathscr{R}\)-boundedness: applications to the Navier-Stokes equations ⋮ Averaging principle and hyperbolic evolution equations ⋮ Periodic solutions for nonresonant parabolic equations on \(\mathbb{R}^N\) with Kato-Rellich type potentials ⋮ Krasnosel'skii type formula and translation along trajectories method on the scale of fractional spaces

Cites Work

• On a generalized Poincaré-Hopf formula in infinite dimensions
• Constrained topological degree and positive solutions of fully nonlinear boundary value problems
• Semigroups of linear operators and applications to partial differential equations
• Geometric theory of semilinear parabolic equations
• On the solution sets of differential inclusions and the periodic problem in Banach spaces.
• Flow invariance for perturbed nonlinear evolution equations
• Topological structure of solution sets of differential inclusions: the constrained case
• The fixed point index for local condensing maps
• Topological degree methods for perturbations of operators generating compact \(C_0\) semigroups
• The generalized degree for compact perturbations of m-accretive operators and applications
• Periodic solutions of the boundary value problem for the nonlinear heat equation
• On the eigenvalue problem for perturbations of nonlinear accretive and monotone operators in banach spaces
• The Leray-Schauder index and the fixed point theory for arbitrary ANRs
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