共查询到20条相似文献,搜索用时 431 毫秒
1.
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
2.
Peter Lesky 《Mathematical Methods in the Applied Sciences》1992,15(7):453-468
We study the initial-boundary value problem for ?t2u(t,x)+A(t)u(t,x)+B(t)?tu(t,x)=f(t,x) on [0,T]×Ω(Ω??n) with a homogeneous Dirichlet boundary condition; here A(t) denotes a family of uniformly strongly elliptic operators of order 2m, B(t) denotes a family of spatial differential operators of order less than or equal to m, and u is a scalar function. We prove the existence of a unique strong solution u. Furthermore, an energy estimate for u is given. 相似文献
3.
For a triple {V, H, V*} of Hilbert spaces, we consider an evolution inclusion of the form u′(t)+A(t)u(t)+δϕ(t, u(t)) ∋
f(t), u(0) = u0, t ∈ (0, T ], where A(t) and ϕ(t, ·), t ∈ [0, T], are a family of nonlinear operators from V to V * and a family of convex lower semicontinuous functionals with common effective domain D(ϕ) ⊂ V. We indicate conditions on the data under which there exists a unique solution of the problem in the space H
1(0, T; V)∩W
∞1 (0, T;H) and the implicit Euler method has first-order accuracy in the energy norm. 相似文献
4.
Explosive solutions of elliptic equations with absorption and nonlinear gradient term 总被引:2,自引:0,他引:2
Marius Ghergu Constantin Niculescu Vicenţiu Rădulescu 《Proceedings Mathematical Sciences》2002,112(3):441-451
Letf be a non-decreasing C1-function such that
andF(t)/f
2
a(t)→ 0 ast → ∞, whereF(t)=∫
0
t
f(s) ds anda ∈ (0, 2]. We prove the existence of positive large solutions to the equationΔu +q(x)|Δu|
a
=p(x)f(u) in a smooth bounded domain Ω ⊂RN, provided thatp, q are non-negative continuous functions so that any zero ofp is surrounded by a surface strictly included in Ω on whichp is positive. Under additional hypotheses onp we deduce the existence of solutions if Ω is unbounded. 相似文献
5.
H. Brézis 《Israel Journal of Mathematics》1971,9(4):513-534
Let φ be a convex l.s.c. function fromH (Hilbert) into ] - ∞, ∞ ] andD(φ)={u ∈H; φ(u)<+∞}. It is proved that for everyu
0 ∈D(φ) the equation − (du/dt)(t ∈ ∂φ(u(t)),u(0)=u
0 has a solution satisfying ÷(du(t)/dt)÷ ≦(c
1/t)+c
2. The behavior ofu(t) in the neighborhood oft=0 andt=+∞ as well as the inhomogeneous equation (du(t)/dt)+∂φ(u(t)) ∈f(t) are then studied. Solutions of some nonlinear boundary value problems are given as applications.
相似文献
6.
Optimal in a certain sense sufficient conditions are given for the existence and uniqueness of ω-periodic solutions of the
nonautonomous ordinary differential equation u
(2m)
=f(t,u,...,u
(m-1)
), where the function f:ℝ×ℝ
m
→ℝ is periodic with respect to the first argument with period ω.
Received: December 21, 1999; in final form: August 12, 2000?Published online: October 2, 2001 相似文献
7.
Given a∈L
1(ℝ) and A the generator of an L
1-integrable family of bounded and linear operators defined on a Banach space X, we prove the existence of almost automorphic solution to the semilinear integral equation u(t)=∫
−∞
t
a(t−s)[Au(s)+f(s,u(s))]ds for each f:ℝ×X→X almost automorphic in t, uniformly in x∈X, and satisfying diverse Lipschitz type conditions. In the scalar case, we prove that a∈L
1(ℝ) positive, nonincreasing and log-convex is already sufficient. 相似文献
8.
Xiaojing Feng Pengcheng Niu Qianqiao Guo 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(4):1119-1131
In this paper, we study the existence and multiplicity of nontrivial solutions for the following second-order Dirichlet nonlinear boundary value problem with odd order derivative: −u″(t)+au′(t)+bu(t)=f(t,u(t)) for all t∈[0,1] with u(0)=u(1)=0, where a,b∈R1, f∈C1([0,1]×R1,R1). By using the Morse theory, we impose certain conditions on f which are able to guarantee that the problem has at least one nontrivial solution, two nontrivial solutions and infinitely many solutions, separately. 相似文献
9.
Qingliu Yao 《Acta Appl Math》2010,110(2):871-883
This paper studies the existence of a positive solution to the second-order periodic boundary value problem
u¢¢(t)+l(t)u(t)=f(t,u(t)), 0 < t < 2p, u(0)=u(2p), u¢(0)=u¢(2p),u^{\prime \prime }(t)+\lambda (t)u(t)=f\bigl(t,u(t)\bigr),\quad 0 10.
Michael T. Lacey 《Journal d'Analyse Mathématique》1995,67(1):199-206
LetT
1 andT
2 be commuting invertible ergodic measure preserving flows on a probability space (X, A, μ). For t = (u,ν) ∈ ℝ2, letT
t
=T
1
u
T
2
v
. LetS
1 denote the unit circle in ℝ2 and σ the rotation invariant unit measure on it. Then, forf∈Lp(X) withp>2, the averagesA
t
f(x) = ∫
s
1
f(T
ts
x)σ(ds) conver the integral off for a. e.x, ast tends to 0 or infinity. This extends a result of R. Jones [J], who treated the case of three or more dimensions. 相似文献
11.
If the second order problem u(t) + Bu(t) + Au(t) = f(t), u(0) =u(0) = 0 has L^p-maximal regularity, 1 〈 p 〈 ∞, the analyticity of the corresponding propagator of the sine type is shown by obtaining the estimates of ‖λ(λ^2 + λB + A)^-1‖ and ‖B(λ^2 + λB + A)^-1‖ for λ∈ C with Reλ 〉 ω, where the constant ω≥ 0. 相似文献
12.
Bruno de Andrade Carlos Lizama 《Journal of Mathematical Analysis and Applications》2011,382(2):761-771
In this paper, a class of nonlinear damped wave equations of the form αu?(t)+u″(t)=βAu(t)+γAu′(t)+f(t,u(t)), t?0, satisfying αβ<γ with prescribed initial conditions are studied. Some sufficient conditions are established for the existence and uniqueness of an asymptotically almost periodic solution. These results have significance in the study of vibrations of flexible structures possessing internal material damping. Finally, an example is presented to illustrate the feasibility and effectiveness of the results. 相似文献
13.
Yasuhiro Fujita Paola Loreti 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(6):771-791
We study a rate of convergence appearing in the long-time behavior of viscosity solutions of the Cauchy problem for the Hamilton–Jacobi
equation
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