共查询到20条相似文献,搜索用时 983 毫秒
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Sergiu Aizicovici Veli-Matti Hokkanen 《Journal of Mathematical Analysis and Applications》2004,292(2):540-557
The solvability of the evolution system v′(t)+B(t)u(t)∋f(t), v(t)∈A(t)u(t), 0<t<T, with the periodic condition v(0)=v(T) is investigated in the case where are bounded, possibly degenerate, subdifferentials and are unbounded subdifferentials. 相似文献
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Quoc-Phong Vu 《Journal of Mathematical Analysis and Applications》2007,334(1):487-501
We study properties of solutions of the evolution equation , where B is a closable operator on the space AP(R,H) of almost periodic functions with values in a Hilbert space H such that B commutes with translations. The operator B generates a family of closed operators on H such that (whenever eiλtx∈D(B)). For a closed subset Λ⊂R, we prove that the following properties (i) and (ii) are equivalent: (i) for every function f∈AP(R,H) such that σ(f)⊆Λ, there exists a unique mild solution u∈AP(R,H) of Eq. (∗) such that σ(u)⊆Λ; (ii) is invertible for all λ∈Λ and . 相似文献
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Jinghua Wang 《Journal of Mathematical Analysis and Applications》2003,284(1):213-235
In this paper we study the generalized Burgers equation ut+(u2/2)x=f(t)uxx, where f(t)>0 for t>0. We show the existence and uniqueness of classical solutions to the initial value problem of the generalized Burgers equation with rough initial data belonging to , as well it is obtained the decay rates of u in Lp norm are algebra order for p∈[1,∞[. 相似文献
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Jie Xiao 《Journal of Differential Equations》2006,224(2):277-295
Let u(t,x) be the solution of the heat equation (∂t-Δx)u(t,x)=0 on subject to u(0,x)=f(x) on Rn. The main goal of this paper is to characterize such a nonnegative measure μ on that f(x)?u(t2,x) induces a bounded embedding from the Sobolev space , p∈[1,n) into the Lebesgue space , q∈(0,∞). 相似文献
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Liangping Jiang 《Journal of Mathematical Analysis and Applications》2007,326(2):1379-1382
The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a function V(t,x), a(‖x‖)?V(t,x)?b(‖x‖) for some a,b∈K, such that for some c∈K. In this paper we prove that if f(t,x) is bounded, is uniformly continuous and bounded, then the condition that can be weakened and replaced by and contains no complete trajectory of , t∈[−T,T], where , uniformly for (t,x)∈[−T,T]×BH. 相似文献
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Zhijun Zhang 《Journal of Mathematical Analysis and Applications》2005,308(2):532-540
By constructing the comparison functions and the perturbed method, it is showed that any solution u∈C2(Ω) to the semilinear elliptic problems Δu=k(x)g(u), x∈Ω, u|∂Ω=+∞ satisfies , where Ω is a bounded domain with smooth boundary in RN; , −2<σ, c0>0, ; g∈C1[0,∞), g?0 and is increasing on (0,∞), there exists ρ>0 such that , ∀ξ>0, , . 相似文献
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We consider a process given by the SDE , t∈[0,T), with initial condition , where T∈(0,∞], α∈R, (Bt)t∈[0,T) is a standard Wiener process, b:[0,T)→R?{0} and σ:[0,T)→(0,∞) are continuously differentiable functions. Assuming , t∈[0,T), with some K∈R, we derive an explicit formula for the joint Laplace transform of and for all t∈[0,T) and for all α∈R. Our motivation is that the maximum likelihood estimator (MLE) of α can be expressed in terms of these random variables. As an application, we show that in case of α=K, K≠0,
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A new result for existence of homoclinic orbits is obtained for the second-order Hamiltonian systems , where t∈R, u∈Rn and W1,W2∈C1(R×Rn,R) and f∈C(R,Rn) are not necessary periodic in t. This result generalizes and improves some existing results in the literature. 相似文献
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J.R. Cannon 《Journal of Mathematical Analysis and Applications》2005,311(1):147-161
The authors study the problem , and u(0,t)=u(1,t)=ψ(t), where ψ(t)=u0 for t2k<t<t2k+1 and ψ(t)=0 for , with t0=0 and the sequence tk is determined by the equations , for , and , for k=2,4,6,… and where 0<m<M. Note that the switching points , are unknown. Existence and uniqueness are demonstrated. Theoretical estimates of the tk and tk+1−tk are obtained and numerical verifications of the estimates are presented. The case of ux(0,t)=ux(1,t)=ψ(t) is also considered and analyzed. 相似文献
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D. Denny 《Journal of Mathematical Analysis and Applications》2010,365(2):467-668
The purpose of this paper is to prove the existence of a unique, classical solution to the nonlinear elliptic partial differential equation −∇⋅(a(u(x))∇u(x))=f(x) under periodic boundary conditions, where u(x0)=u0 at x0∈Ω, with Ω=TN, the N-dimensional torus, and N=2,3. The function a is assumed to be smooth, and a(u(x))>0 for , where G⊂R is a bounded interval. We prove that if the functions f and a satisfy certain conditions, then a unique classical solution u exists. The range of the solution u is a subset of a specified interval . Applications of this work include stationary heat/diffusion problems with a source/sink, where the value of the solution is known at a spatial location x0. 相似文献
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Hongtao Xue 《Journal of Mathematical Analysis and Applications》2011,384(2):439-443
By a sub-supersolution method and a perturbed argument, we improve the earlier results concerning the existence of ground state solutions to a semilinear elliptic problem −Δu+p(x)q|∇u|=f(x,u), u>0, x∈RN, , where q∈(1,2], for some α∈(0,1), p(x)?0, ∀x∈RN, and f:RN×(0,∞)→[0,∞) is a locally Hölder continuous function which may be singular at zero. 相似文献
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For any numerical function we give sufficient conditions for resolving the controlled extension problem for a closed subset A of a normal space X. Namely, if the functions , and satisfy the equality E(f(a),g(a))=h(a), for every a∈A, then we are interested to find the extensions f? and ? of f and g, respectively, such that , for every x∈X. We generalize earlier results concerning E(u,v)=u·v by using the techniques of selections of paraconvex-valued LSC mappings and soft single-valued mappings. 相似文献
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Let (E,D(E)) be a strongly local, quasi-regular symmetric Dirichlet form on L2(E;m) and ((Xt)t?0,(Px)x∈E) the diffusion process associated with (E,D(E)). For u∈De(E), u has a quasi-continuous version and has Fukushima's decomposition: , where is the martingale part and is the zero energy part. In this paper, we study the strong continuity of the generalized Feynman-Kac semigroup defined by , t?0. Two necessary and sufficient conditions for to be strongly continuous are obtained by considering the quadratic form (Qu,Db(E)), where Qu(f,f):=E(f,f)+E(u,f2) for f∈Db(E), and the energy measure μ〈u〉 of u, respectively. An example is also given to show that is strongly continuous when μ〈u〉 is not a measure of the Kato class but of the Hardy class with the constant (cf. Definition 4.5). 相似文献
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Zhijun Zhang 《Journal of Mathematical Analysis and Applications》2005,312(1):33-43
By Karamata regular variation theory and constructing comparison functions, we show the exact asymptotic behaviour of the unique classical solution near the boundary to a singular Dirichlet problem −Δu=k(x)g(u), u>0, x∈Ω, u|∂Ω=0, where Ω is a bounded domain with smooth boundary in RN; g∈C1((0,∞),(0,∞)), , for each ξ>0, for some γ>0; and for some α∈(0,1), is nonnegative on Ω, which is also singular near the boundary. 相似文献