共查询到20条相似文献,搜索用时 15 毫秒
1.
Khalil Ezzinbi 《Journal of Mathematical Analysis and Applications》2007,328(1):344-358
In this work, we study the existence of almost automorphic solutions for some partial functional differential equations. We prove that the existence of a bounded solution on R+ implies the existence of an almost automorphic solution. Our results extend the classical known theorem by Bohr and Neugebauer on the existence of almost periodic solutions for inhomegeneous linear almost periodic differential equations. We give some applications to hyperbolic equations and Lotka-Volterra type equations used to describe the evolution of a single diffusive animal species. 相似文献
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Toka Diagana 《Communications in Nonlinear Science & Numerical Simulation》2012,17(11):4074-4084
In this paper we make extensive use of dichotomy tools and the well-known Schauder fixed point principle to study and obtain the existence of almost automorphic solutions to some nonautonomous damped second-order differential equations. To illustrate our abstract result, we study the existence of almost automorphic solutions to the so-called plate-like equation. 相似文献
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This paper concerns a class of stochastic differential equations driven by fractional Brownian motion. The existence and uniqueness of almost automorphic solutions in distribution are established provided the coefficients satisfy some suitable conditions. To illustrate the results obtained in the paper, a stochastic heat equation driven by fractional Brownian motion is considered. 1 1 The abstract section is available on the university repository site at http://math.dlut.edu.cn/info/1019/4511.htm .
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4.
S. Boulite L. Maniar G. M. N'Gué ré kata 《Proceedings of the American Mathematical Society》2006,134(12):3613-3624
In this work, we use the extrapolation methods to study the existence and uniqueness of almost automorphic solutions to the semilinear boundary differential equation
where generates a hyperbolic -semigroup on a Banach space and are almost automorphic functions which take values in and a ``boundary space' , respectively. These equations are an abstract formulation of partial differential equations with semilinear terms at the boundary, such as population equations, retarded differential equations and boundary control systems. An application to retarded differential equations is given.
where generates a hyperbolic -semigroup on a Banach space and are almost automorphic functions which take values in and a ``boundary space' , respectively. These equations are an abstract formulation of partial differential equations with semilinear terms at the boundary, such as population equations, retarded differential equations and boundary control systems. An application to retarded differential equations is given.
5.
Yoshiyuki Hino 《Journal of Mathematical Analysis and Applications》2003,286(2):741-752
For abstract linear functional differential equations with an almost automorphic forcing term, we establish a result on the existence of almost automorphic solutions, which extends the classical theorem due to Massera on the existence of periodic solutions for linear periodic ordinary differential equations. 相似文献
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We introduce the concepts of Poisson square-mean almost automorphy and almost automorphy in distribution. Under suitable conditions on the coefficients, we establish the existence of solutions which are almost automorphic in distribution for some semilinear stochastic differential equations with infinite dimensional Lévy noise. We further discuss the global asymptotic stability of these solutions. Finally, to illustrate the theoretical results obtained in this paper, we give several examples. 相似文献
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Toka Diagana Gaston Nguerekata Nguyen Van Minh 《Proceedings of the American Mathematical Society》2004,132(11):3289-3298
This paper is concerned with the existence of almost automorphic mild solutions to equations of the form
where generates a holomorphic semigroup and is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying the method of sums of commuting operators used in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to in terms of the imaginary spectrum of and the uniform spectrum of .
where generates a holomorphic semigroup and is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying the method of sums of commuting operators used in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to in terms of the imaginary spectrum of and the uniform spectrum of .
11.
《Applied Mathematics Letters》2007,20(4):462-466
We give in this work some sufficient conditions for the existence and uniqueness of almost automorphic (mild) solutions to some classes of partial evolution equations. Then we use our abstract results to discuss the existence and uniqueness of almost automorphic solutions to some partial differential equations. 相似文献
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In this paper, we study the existence and uniqueness of a weighted pseudo-almost automorphic solution for some nonhomogeneous partial functional differential equations. We use the variation of constants formula developed in Ezzinbi and N’Guérékata (2007) [11] and the spectral decomposition of the phase space to show the main result of this work. To illustrate our main result, we study the existence and uniqueness of a weighted pseudo-almost automorphic solution for some diffusion equations with delay. 相似文献
14.
Hui-Sheng Ding Wei Long Gaston M. NGurkata 《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4158-4164
In this paper, we establish some new theorems about the existence of almost automorphic solutions to nonautonomous evolution equations u′(t)=A(t)u(t)+f(t) and u′(t)=A(t)u(t)+f(t,u(t)) in Banach spaces. As we will see, our results allow for a more general A(t) to some extent. An example is also given to illustrate our results. In addition, by means of an example, we show that one cannot ensure the existence of almost automorphic solutions to u′(t)=A(t)u(t)+f(t) even if the evolution family U(t,s) generated by A(t) is exponentially stable and fAA(X). 相似文献
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Jerome A. Goldstein Gaston M. N'Gué ré kata 《Proceedings of the American Mathematical Society》2005,133(8):2401-2408
We are concerned with the semilinear differential equation in a Banach space ,
where generates an exponentially stable -semigroup and is a function of the form . Under appropriate conditions on and , and using the Schauder fixed point theorem, we prove the existence of an almost automorphic mild solution to the above equation.
where generates an exponentially stable -semigroup and is a function of the form . Under appropriate conditions on and , and using the Schauder fixed point theorem, we prove the existence of an almost automorphic mild solution to the above equation.
16.
M. Baroun L. Maniar G.M. NGurkata 《Nonlinear Analysis: Theory, Methods & Applications》2008,69(7):2114-2124
In this paper, we study the existence and uniqueness of almost periodic and almost automorphic solutions to the semilinear parabolic boundary differential equations where AAm|kerL generates a hyperbolic analytic semigroup on a Banach space X. The functions h and are defined on some intermediate subspaces Xβ,0<β<1, and take values in X and in a boundary space ∂X respectively. 相似文献
17.
This paper is concerned with the problem of explosive solutions for a class of stochastic differential equations. Our main results are presented as two theorems. Theorem 1 is concerned with the existence of explosive solutions with positive probability under certain sufficient conditions. With some additional mild conditions, it is shown in Theorem 2 that the explosion will occur almost surely. The methods of auxiliary functions and cycles are used in the proofs. Several remarks about their applications are given. 相似文献
18.
William Dimbour 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(6):2351-2357
Using spectral theory we obtain sufficient conditions for the almost automorphy of bounded solutions to differential equations with piecewise constant argument of the form x′(t)=A(t)x([t])+f(t),t∈R, where A(t) is an almost automorphy operator, f(t) is an X-valued almost automorphic function and X is a finite dimensional Banach space. 相似文献
19.
《Nonlinear Analysis: Theory, Methods & Applications》2010,72(12):e432-e435
In this paper we give some sufficient conditions for ensuring the existence and uniqueness of a mild almost automorphic solution to a second-order semilinear evolution equation in a Banach space. We also present some properties of the (new) notion of a uniform spectrum of bounded functions. 相似文献