On the Periodic Mild Solutions to Complete Higher Order Differential Equations
نویسنده
چکیده
where Aj are linear, closed operators on a Banach space E and f is a function from [0, T ] to E. The asymptotic behavior and, in particular, the periodicity of solutions of the higher order differential equation u(t) = Au(t) + f(t), 0 ≤ t ≤ T, (1.2) has been an subject of intensive study for recent decades. When n = 1, it is well-known [7] that, if A is an n×n matrix on C, then (1.2) admits a unique §2000 AMS Subject Classification: Primary 34 G 10, 34 K 06, Secondary 47 D 06.
منابع مشابه
ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR CERTAIN NON-LINEAR DIFFERENTIAL EQUATIONS
Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...
متن کاملOn the Periodic Mild Solutions to Complete Higher Order Differential Equations on Banach Spaces
For the complete higher order differential equation
متن کاملOn the Regularity of Mild Solutions to Complete Higher Order Differential Equations on Banach Spaces
For the complete higher order differential equation u(t) = Σn−1 k=0Aku (t) + f(t), t ∈ R (*) on a Banach space E, we give a new definition of mild solutions of (*). We then characterize the regular admissibility of a translation invariant subspace M of BUC(R,E) with respect to (*) in terms of solvability of the operator equation Σn−1 j=0AjXD j −XD = C. As application, almost periodicity of mild...
متن کاملON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *
The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.
متن کامل$L^p$-existence of mild solutions of fractional differential equations in Banach space
We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work.
متن کاملOn the Mild Solutions of Higher-order Differential Equations in Banach Spaces
For the higher-order abstract differential equation u(n)(t) = Au(t) + f (t), t ∈ R, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace of BUC(R,E) with respect to the above-mentioned equation in terms of solvability of the operator equation AX −X n = C. As applications, periodicity and almost periodicity of mild solutio...
متن کامل