Results 11 to 20 of about 23 (23)
On some classes of almost periodic functions in abstract spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 61, Page 3237-3247, 2004., 2004 We deal with C(n)‐almost periodic functions taking values in a Banach space. We give several properties of such functions, in particular, we investigate their behavior in view of differentiation as well as integration. The superposition operator acting in the space of such functions is also under consideration.
Dariusz Bugajewski +1 more
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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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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
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Bounded solutions of nonlinear Cauchy problems
Abstract and Applied Analysis, Volume 7, Issue 12, Page 637-661, 2002., 2002 For a given closed and translation invariant subspace Y of the bounded and uniformly continuous functions, we will give criteria for the existence of solutions u ∈ Y to the equation u′(t) + A(u(t)) + ωu(t)∍f(t), t ∈ ℝ, or of solutions u asymptotically close to Y for the inhomogeneous differential equation u′(t) + A(u(t)) + ωu(t)∍f(t), t > 0, u(0) = u0,
Josef Kreulich
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Ergodicity and asymptotically almost periodic solutions of some differential equations
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 12, Page 787-801, 2001., 2001 Using ergodicity of functions, we prove the existence and uniqueness of (asymptotically) almost periodic solution for some nonlinear differential equations. As a consequence, we generalize a Massera’s result. A counterexample is given to show that the ergodic condition cannot be dropped.
Chuanyi Zhang
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On the existence of solutions for a class of first‐order differential equations
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 1, Page 1-10, 2001., 2001 A system of first‐order differential equations with linear constraint is studied. Existence theorems for the solution are proved under some conditions. Some uniqueness and dependence results for the system are also obtained. Some applications are given.
Kamel Al-Khaled
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International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 9, Page 521-534, 2001., 2001 We consider abstract differential equations of the form u′(t) = Au(t) + f(t) or u″(t) = Au(t) + f(t) in Banach spaces X, where f(⋅), ℝ → X is almost‐periodic, while A is a linear operator, 𝒟(A) ⊂ X → X. If the solution u(⋅) is likewise almost‐periodic, ℝ → X, we establish connections between their Bohr‐transforms, uˆ(λ) and fˆ(λ).
Samuel Zaidman
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Abstract and Applied Analysis, Volume 5, Issue 4, Page 245-263, 2000., 2000 We study evolution semigroups associated with nonautonomous functional differential equations. In fact, we convert a given functional differential equation to an abstract autonomous evolution equation and then derive a representation theorem for the solutions of the underlying functional differential equation. The representation theorem is then used to
Bernd Aulbach, Nguyen Van Minh
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Abstract and Applied Analysis, Volume 4, Issue 3, Page 169-194, 1999., 1999 We investigate the asymptotic properties of the inhomogeneous nonautonomous evolution equation (d/dt)u(t) = Au(t) + B(t)u(t) + f(t), t ∈ ℝ, where (A, D(A)) is a Hille‐Yosida operator on a Banach space X, B(t), t ∈ ℝ, is a family of operators in ℒ(D(A)¯,X) satisfying certain boundedness and measurability conditions and f∈L loc 1(ℝ,X).
Gabriele Gühring, Frank Räbiger
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Almost periodic solutions for Abel equations
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 727-735, 1997., 1997 Using the Liapunov function method, the existence of almost periodic solutions of a scalar differential equation is discussed The results for the scalar differential equation are then applied to prove the existence and stability of almost periodic solutions of Abel differential equations We obtain several interesting results which improve the results ...
Zeng Weiyao +3 more
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