Results 11 to 20 of about 55 (54)
On the decoupled Markov group conjecture
Bulletin of the London Mathematical Society, Volume 53, Issue 1, Page 240-247, February 2021., 2021 Abstract The Markov group conjecture, a long‐standing open problem in the theory of Markov processes with countable state space, asserts that a strongly continuous Markov semigroup T=(Tt)t∈[0,∞) on ℓ1 has bounded generator if the operator T1 is bijective. Attempts to disprove the conjecture have often aimed at glueing together finite‐dimensional matrix
Jochen Glück
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On almost automorphic solutions of linear operational‐differential equations
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 22, Page 1179-1182, 2004., 2004 We prove almost periodicity and almost automorphy of bounded solutions of linear differential equations x′(t) = Ax(t) + f(t) for some class of linear operators acting in a Banach space.
Gaston M. N′Guérékata
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On a higher‐order evolution equation with a Stepanov‐bounded solution
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 72, Page 3959-3964, 2004., 2004 We study strong solutions u : ℝ → X, a Banach space X, of the nth‐order evolution equation u(n) − Au(n−1) = f, an infinitesimal generator of a strongly continuous group A : D(A)⊆X → X, and a given forcing term f : ℝ → X. It is shown that if X is reflexive, u and u(n−1) are Stepanov‐bounded, and f is Stepanov almost periodic, then u and all derivatives ...
Aribindi Satyanarayan Rao
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International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 45, Page 2401-2422, 2004., 2004 Necessary and sufficient conditions for a scalar type spectral operator in a Banach space to be a generator of an infinite differentiable or a Gevrey ultradifferentiable C0‐semigroup are found, the latter formulated exclusively in terms of the operator′s spectrum.
Marat V. Markin
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The fundamental solutions for fractional evolution equations of parabolic type
International Journal of Stochastic Analysis, Volume 2004, Issue 3, Page 197-211, 2004., 2004 The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is
Mahmoud M. El-Borai
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Hyperbolic differential‐operator equations on a whole axis
Abstract and Applied Analysis, Volume 2004, Issue 2, Page 99-113, 2004., 2004 We give an abstract interpretation of initial boundary value problems for hyperbolic equations such that a part of initial boundary value conditions contains also a differentiation on the time t of the same order as equations. The case of stable solutions of abstract hyperbolic equations is treated.
Yakov Yakubov
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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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