Results 31 to 40 of about 320 (70)
On the mild solutions of higher‐order differential equations in Banach spaces
Abstract and Applied Analysis, Volume 2003, Issue 15, Page 865-880, 2003., 2003 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 ℳ of BUC(ℝ, E) with respect to the above‐mentioned equation in terms of solvability of the operator equation AX − X𝒟n = C.
Nguyen Thanh Lan
wiley +1 more source
Abstract Cauchy Problem of Conformable Type and Operator Ideals in Hilbert Space
Journal of Function Spaces, Volume 2025, Issue 1, 2025.In this paper, we focus our study on the fractional homogeneous abstract Cauchy problems of conformable type, wβ(t) = Uw(t), t ∈ [0, T), T ≤ ∞, w(0) = x, where U is a linear operator that generates a fractional β‐semigroup on a Hilbert space H. In fact, we gave an answer to the question if U is the infinitesimal generator of a conformable β‐semigroup ...
Sharifa Al−Sharif +3 more
wiley +1 more source
Large diffusivity finite‐dimensional asymptotic behaviour of a semilinear wave equation
Journal of Applied Mathematics, Volume 2003, Issue 8, Page 409-427, 2003., 2003 We study the effects of large diffusivity in all parts of the domain in a linearly damped wave equation subject to standard zero Robin‐type boundary conditions. In the linear case, we show in a given sense that the asymptotic behaviour of solutions verifies a second‐order ordinary differential equation.
Robert Willie
wiley +1 more source
Existence of positive periodic solutions for evolution equations with delay in ordered Banach spaces
Open MathematicsThe main focus of this study is to discuss the existence of positive ω\omega -periodic mild solutions for evolution equation with delay in an ordered Banach space EE. Under the ordered conditions of the growth exponent of the nonlinearity gg with respect
Zhang Jing, Gou Haide
doaj +1 more source
Solvable Systems of Linear Differential Equations
, 2009 The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations.
A. Durmus +18 more
core +1 more source
Journal of Mathematics, Volume 2025, Issue 1, 2025.This paper investigates an abstract nonhomogeneous backward Cauchy problem governed by an unbounded linear operator in a Hilbert space H. The coefficient operator in the equation is assumed to be unbounded, self‐adjoint, positive, and to possess a discrete spectrum, with data prescribed at the final time t = T.
Nihed Teniou, Xian-Ming Gu
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 9, Page 573-578, 2002., 2002 In a Banach space, if u is a Stepanov almost periodic solution of a certain nth‐order infinitesimal generator and time‐dependent operator differential equation with a Stepanov almost periodic forcing function, then u, u′, …, u (n−2) are all strongly almost periodic and u (n−1) is weakly almost periodic.
Aribindi Satyanarayan Rao
wiley +1 more source
A Katznelson-Tzafriri theorem for measures
, 2014 This article generalises the well-known Katznelson-Tzafriri theorem for a $C_0$-semigroup $T$ on a Banach space $X$, by removing the assumption that a certain measure in the original result be absolutely continuous.
Seifert, David
core +1 more source
A note on the spectral operators of scalar type and semigroups of bounded linear operators
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 10, Page 635-640, 2002., 2002 It is shown that, for the spectral operators of scalar type, the well‐known characterizations of the generation of C0‐ and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup ...
Marat V. Markin
wiley +1 more source
When unit groups of continuous inverse algebras are regular Lie groups
, 2012 It is a basic fact in infinite-dimensional Lie theory that the unit group G(A) of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group G(A) is regular in Milnor's sense.
Glockner, Helge, Neeb, Karl-Hermann
core +1 more source