Results 21 to 30 of about 65 (61)
Abstract and Applied Analysis, Volume 2004, Issue 12, Page 1007-1018, 2004., 2004 In the class of scalar type spectral operators in a complex Banach space, a characterization of the generators of analytic C0‐semigroups in terms of the analytic vectors of the operators is found.
Marat V. Markin
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An inverse problem for a second‐order differential equation in a Banach space
Abstract and Applied Analysis, Volume 2004, Issue 12, Page 997-1005, 2004., 2004 We consider the problem of determining the unknown term in the right‐hand side of a second‐order differential equation with unbounded operator generating a cosine operator function from the overspecified boundary data. We obtain necessary and sufficient conditions of the unique solvability of this problem in terms of location of the spectrum of the ...
Y. Eidelman
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Abstract and Applied Analysis, Volume 2004, Issue 10, Page 881-896, 2004., 2004 Let u be a given bounded uniformly continuous mild solution of a higher‐order abstract functional differential equation of delay or advance type. We give a so‐called Massera‐type criterion for the existence of a mild solution, which is a “spectral component” of u with spectrum similar to the one of the forcing term f.
Nguyen Van Minh, Ha Binh Minh
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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
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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
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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 +3 more
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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
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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
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Spectral mapping theorems for evolutions semigroups on spaces of almost periodic functions [PDF]
, 2004 unavailable at this time... Mathematics Subject Classification (2000): 47D06, 34G10, 34C27 Quaestiones Mathematicae 25 (2002), 191 ...
Räbiger, Frank, Hutter, Walter
core
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
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