Results 41 to 50 of about 378 (71)

On the Lw2‐boundedness of solutions for products of quasi‐integro differential equations

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 10, Page 639-659, 2003., 2003
Given a general quasi‐differential expressions τ1, τ2, …, τn each of order n with complex coefficients and their formal adjoints are τ1+,τ2+,…,τn+ on [0, b), respectively, we show under suitable conditions on the function F that all solutions of the product of quasi‐integrodifferential equation [∏j=1nτj]y=wF(t,y,∫0tg(t,s,y,y′,…,y(n2−1)(s))ds) on [0, b),
Sobhy El-Sayed Ibrahim
wiley   +1 more source

Almost periodic solutions of periodic linear partial functional differential equations

, 2018
We study conditions for the abstract periodic linear functional differential equation $\dot{x}=Ax+F(t)x_t+f(t)$ to have almost periodic with the same structure of frequencies as $f$.
Luong, Vu Trong, Van Minh, Nguyen
core   +1 more source

Linear neutral partial differential equations: a semigroup approach

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 23, Page 1433-1445, 2003., 2003
We study linear neutral PDEs of the form (∂/∂t)Fut = BFut + Φut, t ≥ 0; u0(t) = φ(t), t ≤ 0, where the function u(⋅) takes values in a Banach space X. Under appropriate conditions on the difference operator F and the delay operator Φ, we construct a C0‐semigroup on C0(ℝ−, X) yielding the solutions of the equation.
Rainer Nagel, Nguyen Thieu Huy
wiley   +1 more source

Existence of the Conformable Double Laplace–Elzaki Transform and Applications

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
In this study, we introduce and establish the existence of the conformable fractional Laplace–Elzaki transform (CLET), a new integral transform designed to handle fractional‐order problems. Several fundamental properties and theorems of the CLET are derived and discussed.
Zaid Zaqzaq, Sharifa Al-Sharif, Waseem Ghazi Alshanti, Zhihua Zhang   +3 more
wiley   +1 more source

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

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

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, Ghandi Rababa, Mesfer H. Alqahtani, Yusuf Gurefe   +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 Mathematics
The 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

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