共查询到20条相似文献,搜索用时 15 毫秒
1.
Xiong Li 《Proceedings of the American Mathematical Society》2004,132(7):2057-2066
In this paper we will study the boundedness of all solutions for second-order differential equations
where and satisfies the sublinear growth condition. Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible mappings. Under some suitable conditions we then obtain the existence of invariant tori and thus the boundedness of all solutions.
where and satisfies the sublinear growth condition. Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible mappings. Under some suitable conditions we then obtain the existence of invariant tori and thus the boundedness of all solutions.
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In this paper we are concerned with the boundedness of all solutions of the second order differential equations
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Xiaojing Yang 《Journal of Mathematical Analysis and Applications》2004,294(1):122-140
In this paper, we are concerned with the problem of boundedness of solutions for the following nonlinear p-Laplacian:
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LI Xiong 《中国科学A辑(英文版)》2001,44(2):137-144
We are concerned with the boundedness of all the solutions for second order differential equation
, wheref(x) andg(x) are odd, e( t) is odd and 1-periodic, andg(x) satisfies
相似文献
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In this paper we consider the problem of the boundedness of all solutions for the reversible system
6.
In this paper, the boundedness of all solutions of the oscillator
is discussed, where ω is a positive constant, f(x,y),?(x) and p(t) are smooth functions, and p(t)=p(t+2π). 相似文献
x″+f(x,x′)+ω2x+?(x)=p(t)
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LI Xiong 《数学年刊B辑(英文版)》2001,22(1):31-46
51. IntroductionThe boundedness problem of solutions of the following nonlinear scalar differelltial equa-nons of second order..x f(x, t)ic g(x, t) = 0 (1'1)has been widely investigated by many authors since the 1940's, where f(x, t 1) = j(x, t),g(x, t 1) = g(x, t).When j(x, t) = 0, Equation (1.1) is a conservative system and takes the following form..x g(x, t) ~ 0. (1'2)The first contribution of the boundedness of all the solutions of Equation (1.2) is due toMorrislll, whO proved … 相似文献
8.
In this paper, we prove that the second order differential equation d^2x/dt^2+x^2n_1f(x)+p(t)=0with p(t + 1) = p(t), f(x + T) = f(x) smooth and f(x) 〉 0, possesses Lagrangian stability despite of the fact that the monotone twist condition is violated. 相似文献
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Bin Liu 《Transactions of the American Mathematical Society》2001,353(4):1567-1585
In this paper, we are concerned with the boundedness of all the solutions and the existence of quasi-periodic solutions for second order differential equations
where the 1-periodic function is a smooth function and satisfies sublinearity:
11.
This paper deals with the relation between isochronicity and first integral for a class of reversible systems: , , which associates to the first integral of the form H(x,y)=F(x)y2+G(x). Two necessary and sufficient conditions are given to characterize isochronicity for these systems. Moreover, we apply these results to show that there exists a class of polynomial reversible systems of degree n with isochronous center for any n. 相似文献
12.
汪小明 《数学年刊A辑(中文版)》2015,36(4):355-366
通过引进合适的作用-角变量变换并结合新的估计方法,对次线性可逆系统的Poincare映射,应用推广的平面可逆系统的Aubry-Mather定理,在系统光滑性为C~1的情形下,获得了一类次线性可逆系统的Aubry-Mather集存在的充分条件. 相似文献
13.
In this paper, we solve an open problem appeared in Cao et al. (2009) concerning the uniqueness of solutions for a sublinear pseudo-parabolic Cauchy problem. In the zero initial case, we obtain the class of all non-trivial global solutions, whereas, the uniqueness of global solutions is established when the initial condition is non-zero. A lower grow-up rate of solutions is also obtained. 相似文献
14.
Svitlana P. Rogovchenko 《Journal of Mathematical Analysis and Applications》2003,279(1):121-134
In this paper, we are concerned with a class of nonlinear second-order differential equations with a nonlinear damping term. Passage to more general class of equations allows us to remove a restrictive condition usually imposed on the nonlinearity, and, as a consequence, our results apply to wider classes of nonlinear differential equations. Two illustrative examples are considered. 相似文献
15.
Existence of periodic solutions of nonlinear systems with nonlinear boundary conditions 总被引:1,自引:0,他引:1
In this paper we consider the periodic solutions of nonlinear parabolic systems with nonlinear boundary conditions. By constructing the Poincare operator, we obtain the existence of
-periodic weak solutions under some reasonable assumptions. 相似文献
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Marius Ghergu 《Journal of Mathematical Analysis and Applications》2005,311(2):635-646
We establish several results related to existence, nonexistence or bifurcation of positive solutions for the boundary value problem −Δu+K(x)g(u)+a|∇u|=λf(x,u) in Ω, u=0 on ∂Ω, where Ω⊂RN(N?2) is a smooth bounded domain, 0<a?2, λ is a positive parameter, and f is smooth and has a sublinear growth. The main feature of this paper consists in the presence of the singular nonlinearity g combined with the convection term a|∇u|. Our approach takes into account both the sign of the potential K and the decay rate around the origin of the singular nonlinearity g. The proofs are based on various techniques related to the maximum principle for elliptic equations. 相似文献
20.
Xiangsheng Xu 《Journal of Mathematical Analysis and Applications》2010,371(1):134-145
In this paper we obtain the boundedness of solutions to a time-dependent semiconductor model with variable electron mobility. The proof is based upon an interpolation inequality which is of interest on its own right. 相似文献