Parabolicity of second order differential equations in Hubert space.
Parametrized relaxation for evolution inclusions of the subdifferential type
In this paper we consider parametric nonlinear evolution inclusions driven by time-dependent subdifferentials. First we prove some continuous dependence results for the solution set (of both the convex and nonconvex problems) and for the set of solution-selector pairs (of the convex problem). Then we derive a continuous version of the “Filippov-Gronwall” inequality and using it, we prove the parametric relaxation theorem. An example of a parabolic distributed parameter system is also worked out...
Periodic and almost periodic solutions for multi-valued differential equations in Banach spaces.
Periodic and aqlmost-periodic solutions of semihnear equations in Banach spaces.
Periodic boundary value problem in Hilbert space for differential equation of second order with reflection of the argument
Periodic in distribution solution for a telegraph equation.
Periodic problems and problems with discontinuities for nonlinear parabolic equations
In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that...
Periodic problems for ODEs via multivalued Poincaré operators
We shall consider periodic problems for ordinary differential equations of the form where satisfies suitable assumptions. To study the above problem we shall follow an approach based on the topological degree theory. Roughly speaking, if on some ball of , the topological degree of, associated to (), multivalued Poincaré operator turns out to be different from zero, then problem () has solutions. Next by using the multivalued version of the classical Liapunov-Krasnoselskǐ guiding potential...
Periodic Solutions for Nonlinear Evolution Equations with Non-instantaneous Impulses
In this paper, we consider periodic solutions for a class of nonlinear evolution equations with non-instantaneous impulses on Banach spaces. By constructing a Poincaré operator, which is a composition of the maps and using the techniques of a priori estimate, we avoid assuming that periodic solution is bounded like in [1-4] and try to present new sufficient conditions on the existence of periodic mild solutions for such problems by utilizing semigroup theory and Leray-Schauder's fixed point theorem....
Periodic solutions for nonlinear evolution inclusions
In this paper we prove the existence of periodic solutions for a class of nonlinear evolution inclusions defined in an evolution triple of spaces and driven by a demicontinuous pseudomonotone coercive operator and an upper semicontinuous multivalued perturbation defined on with values in . Our proof is based on a known result about the surjectivity of the sum of two operators of monotone type and on the fact that the property of pseudomonotonicity is lifted to the Nemitsky operator, which we...
Periodic solutions for quasilinear vector differential equations with maximal monotone terms
We consider a quasilinear vector differential equation with maximal monotone term and periodic boundary conditions. Approximating the maximal monotone operator with its Yosida approximation, we introduce an auxiliary problem which we solve using techniques from the theory of nonlinear monotone operators and the Leray-Schauder principle. To obtain a solution of the original problem we pass to the limit as the parameter λ > 0 of the Yosida approximation tends to zero.
Periodic solutions of abstract and partial differential equations with deviation
Periodic solutions of abstract differential equations: the Fourier method
Periodic solutions of an abstract third-order differential equation
Using operator valued Fourier multipliers, we characterize maximal regularity for the abstract third-order differential equation αu'''(t) + u''(t) = βAu(t) + γBu'(t) + f(t) with boundary conditions u(0) = u(2π), u'(0) = u'(2π) and u''(0) = u''(2π), where A and B are closed linear operators defined on a Banach space X, α,β,γ ∈ ℝ₊, and f belongs to either periodic Lebesgue spaces, or periodic Besov spaces, or periodic Triebel-Lizorkin spaces.
Periodic solutions of degenerate differential equations in vector-valued function spaces
Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multiplier theorems, we obtain necessary and sufficient conditions for the existence and uniqueness of periodic solutions to the equation d/dt(Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our results are obtained in the scales of periodic Besov and periodic Lebesgue vector-valued spaces.
Periodic Solutions of Differential Equations in Banach Spaces.
Periodic solutions of infinite dimensional Riccati Equations
Si da un risultato di esistenza di soluzioni periodiche per una equazione di Riccati in dimensione infinita.
Periodic solutions of semilinear impulsive periodic system with time-varying generating operators on Banach space.
Periodic solutions to a singular abstract differential equation
Periodic solutions to abstract differential equations