Periodic solutions to certain evolution inequalities
Periodic solutions to evolution equations: existence, conditional stability and admissibility of function spaces
We prove the existence and conditional stability of periodic solutions to semilinear evolution equations of the form u̇ = A(t)u + g(t,u(t)), where the operator-valued function t ↦ A(t) is 1-periodic, and the operator g(t,x) is 1-periodic with respect to t for each fixed x and satisfies the φ-Lipschitz condition ||g(t,x₁) - g(t,x₂)|| ≤ φ(t)||x₁-x₂|| for φ(t) being a real and positive function which belongs to an admissible function space. We then apply the results to study the existence, uniqueness...
Périodicite des solutions d'equations differentielles dans les espaces de Banach.
Periodicity of mild solutions to higher order differential equations in Banach spaces.
Perron conditions and uniform exponential stability of linear skew-product semiflows on locally compact spaces.
Persistence of Crandall-Rabinowitz type bifurcations under small perturbations.
Perturbation stochastique de processus de rafle
Lors de cet exposé, nous nous intéressons à l’étude de perturbations stochastiques de certaines inclusions différentielles du premier ordre : les processus de rafle par des ensembles uniformément prox-réguliers. Ce travail nous amène à combiner la théorie des processus de rafle et celle traitant de la reflexion d’un mouvement brownien sur la frontière d’un ensemble. Nous donnerons des résultats traitant du caractère bien-posé de ces inclusions différentielles stochastiques et de leur stabilité.
Perturbation theorems for maximal -regularity
Perturbations numériques des évolutions parabolique et hyperbolique
Perturbations of Positive Semigroups and Applications to Population Genetics.
Points singuliers d'équations différentielles
Porous medium equation and fast diffusion equation as gradient systems
We show that the Porous Medium Equation and the Fast Diffusion Equation, , with , can be modeled as a gradient system in the Hilbert space , and we obtain existence and uniqueness of solutions in this framework. We deal with bounded and certain unbounded open sets and do not require any boundary regularity. Moreover, the approach is used to discuss the asymptotic behaviour and order preservation of solutions.
Positive solutions for a class of fourth-order boundary value problems in Banach spaces.
Positive solutions for a high-order multi-point boundary-value problem in Banach spaces.
Positive solutions for impulsive equations of third order in Banach space.
Positive solutions for second-order multi-point boundary-value problems at resonance in Banach spaces.
Positive solutions of singular multipoint boundary value problems for systems of nonlinear second-order differential equations on infinite intervals in Banach spaces.
Positivity and stability for a system of transport equations with unbounded boundary perturbations.
Power Series Solutions of Algebraic Differential Equations.
Poznámka k aplikacím Laplaceovy transformace na abstraktní diferenciální rovnice parabolického typu