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Some sufficient conditions for the existence and uniqueness of pseudo-almost periodic (mild) solutions to some classes of partial evolution equations are given. We then make use of our abstract results to discuss the existence of pseudo-almost periodic solutions to some partial differential equations. 相似文献
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The paper considers some new classes of functions called weighted pseudo-almost periodic functions, which implement in a natural fashion the classical pseudo-almost periodic functions due to Zhang. Properties of these weighted pseudo-almost periodic functions are discussed, including a composition result for weighted pseudo-almost periodic functions. The results obtained are subsequently utilized to study the existence and uniqueness of a weighted pseudo-almost periodic solution to the heat equation with Dirichlet conditions. 相似文献
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The paper revisits the concept of Sp-pseudo-almost periodicity recently introduced by the author. In particular, we study the existence of pseudo-almost periodic solutions to some nonautonomous differential equations in the case when the semilinear forcing term is both continuous and Sp-pseudo-almost periodic for p>1. Applications include the existence of pseudo-almost periodic solutions to the heat equation with a forcing term, which is Sp-pseudo-almost periodic and jointly continuous. 相似文献
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Jin Liang Gaston M. N’Guérékata Ti-Jun Xiao Jun Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2009
This paper is concerned with some properties of pseudo-almost automorphic functions, which are more general and complicated than pseudo-almost periodic functions. Using these properties, we establish an existence and uniqueness theorem for pseudo-almost automorphic mild solutions to semilinear differential equations in a Banach space. 相似文献
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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
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Toka Diagana 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(2):600-615
In this paper, under Acquistapace-Terreni conditions, we make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of weighted pseudo-almost periodic solutions to some classes of nonautonomous partial evolution equations. Applications include the existence of weighted pseudo-almost periodic solutions to a nonautonomous heat equation with gradient coefficients. 相似文献
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Zhanrong HuZhen Jin 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(1):244-252
We obtain new existence and uniqueness theorems of pseudo almost periodic mild solutions to nonautonomous neutral partial evolution equations
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Dariusz Bugajewski Xiao-Xiong Gan Piotr Kasprzak 《Nonlinear Analysis: Theory, Methods & Applications》2012
In the first part of the paper we examine mappings of higher order from a general point of view, that is, in normed spaces of bounded real-valued functions defined on R. Particular attention is paid to the relation of such mappings with the so-called autonomous superposition operators. Next we investigate mappings of higher order in Banach spaces of almost periodic functions and their perturbations. We also give necessary and sufficient conditions guaranteeing that a nonautonomous superposition operator acts in the space of almost periodic functions in the sense of Levitan and is uniformly continuous. In the Banach space of bounded almost periodic functions in the sense of Levitan we discuss mappings of higher order and a convolution operator. Some applications to nonlinear differential and integral equations are given. 相似文献
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We study the fractional differential equation (*) Dαu(t) + BDβu(t) + Au(t) = f(t), 0 ? t ? 2π (0 ? β < α ? 2) in periodic Lebesgue spaces Lp(0, 2π; X) where X is a Banach space. Using functional calculus and operator valued Fourier multiplier theorems, we characterize, in UMD spaces, the well posedness of (*) in terms of R‐boundedness of the sets {(ik)α((ik)α + (ik)βB + A)?1}k∈ Z and {(ik)βB((ik)α + (ik)βB + A)?1}k∈ Z . Applications to the fractional problems with periodic boundary condition, which includes the time diffusion and fractional wave equations, as well as an abstract version of the Basset‐Boussinesq‐Oseen equation are treated. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
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Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations
Ravi P. Agarwal Bruno de Andrade Claudio Cuevas 《Nonlinear Analysis: Real World Applications》2010,11(5):3532-3554
We study the existence and uniqueness of a weighted pseudo-almost periodic (mild) solution to the semilinear fractional equation , , where is a linear operator of sectorial negative type. This article also deals with the existence of these types of solutions to abstract partial evolution equations. 相似文献
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We study the existence of almost periodic (resp., pseudo-almost periodic) mild solutions for fractional differential and integro-differential equations in the case when the forcing term belongs to the class of Stepanov almost (resp., Stepanov-like pseudo-almost) periodic functions. 相似文献
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In this paper we consider the existence and uniqueness of positive periodic solution for the periodic equation y′(t)=−a(t)y(t)+λh(t)f(y(t−τ(t))). By the eigenvalue problems of completely continuous operators and theory of α-concave or −α-convex operators and its eigenvalue, we establish some criteria for existence and uniqueness of positive periodic solution of above functional differential equations with parameter. In particular, the unique solution yλ(t) of the above equation depends continuously on the parameter λ. Finally, as an application, we obtain sufficient condition for the existence of positive periodic solutions of the Nicholson blowflies model. 相似文献
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Nikolay Kutev Natalia Kolkovska Milena Dimova 《Mathematical Methods in the Applied Sciences》2016,39(9):2287-2297
A new ordinary differential inequality without global solutions is proposed. Comparison with similar differential inequalities in the well‐known concavity method is performed. As an application, finite time blow up of the solutions to nonlinear Klein–Gordon equation and generalized Boussinesq equation is proven. The initial energy is arbitrary high positive. The structural conditions on the initial data generalize the assumptions used in the literature for the time being. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Zdzisław Denkowski Leszek Gasiński Nikolaos S. Papageorgiou 《Nonlinear Analysis: Theory, Methods & Applications》2007
In this paper we study semilinear hemivariational inequalities at resonance. Assuming a partially anticoercive nonsmooth potential we prove an existence and a multiplicity theorem. The method of the proof is variational and in the multiplicity result, we employ the nonsmooth local linking theorem. 相似文献
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Paul H. Bezandry 《Applicable analysis》2013,92(7):819-827
The article introduces and studies the concept of p-mean almost periodicity for stochastic processes. Our abstract results are, subsequently, applied to studying the existence of square-mean almost periodic solutions to some semilinear stochastic equations. 相似文献
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T.T. Khanh 《Journal of Differential Equations》2010,249(10):2440-2475
We investigate the analyticity of solutions to semilinear elliptic equations degenerated on a submanifold. We introduce a new weighted Sobolev space which is appropriate for studying such equations. The technique for linear equations using cut-off functions cannot be applied and we need to use a representation formula which requires a fundamental solution. 相似文献