Boundedness of solutions for reversible system via Moser's twist theorem

In this paper we consider the problem of the boundedness of all solutions for the reversible system

     

Boundedness of solutions for semilinear reversible systems

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.

     

Boundedness of solutions for second order differential equations with asymmetric nonlinearity

In this paper we are concerned with the boundedness of all solutions of the second order differential equations

     

Boundedness of solutions for asymmetric Duffing equations

In this paper, we are concerned with the boundedness of all the solutions and the existence of quasiperiodic solutions for some Duffing equations , where e(t) is of period 1, and g : R → R possesses the characters: g(x) is superlinear when x ? d₀, d₀ is a positive constant and g(x) is semilinear when x ? 0.     

Boundedness of solutions of nonlinear systems of differential equations

We first give an example to illustrate that the results in [12] concerning the boundedness of solutions of nonlinear oscillatory equations are not true. And then we obtain sufficient or necessary conditions for the boundedness of solutions of the nonlinear system of differential equations

Boundedness for sublinear reversible systems with a nonlinear damping and periodic forcing term

In this paper, we are concerned with the sublinear reversible systems with a nonlinear damping and periodic forcing term

x^″+f(x)g(x^′)+γ|x|^α−1x=p(t),     

Boundedness of Solutions for Duffing Equation with Low Regularity in Time

It is shown that all solutions are bounded for Duffing equation x+ x~(2n+1)+2∑i=nPj(t)x~j= 0, provided that for each n + 1 ≤ j ≤ 2 n, P_j ∈ C~y(T~1) with γ 1-1/n and for each j with 0 ≤ j ≤ n, Pj ∈ L(T~1) where T~1= R/Z.     

一类二阶非线性常微分方程解的有界性

本文研究了下列微分方程解的有界性，其中关于ｔ是１－周期的而关于ｘ是拟周期的．     

Boundedness of solutions to a time-dependent semiconductor model

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.     

On Littlewood's boundedness problem for sublinear Duffing equations

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:

     

Boundedness of extremal solutions in dimension 4

In this paper we establish the boundedness of the extremal solution u^∗$u^{\ast }$ in dimension N=4$N=4$ of the semilinear elliptic equation −Δu=λf(u)$-\Delta u=\lambda f\left(u\right)$, in a general smooth bounded domain Ω⊂R^N$\Omega \subset {\mathbb{R}}^N$, with Dirichlet data u_|∂Ω=0$u{|}_{\partial \Omega }=0$, where f$f$ is a C¹$C^1$ positive, nondecreasing and convex function in [0,∞)$[0,\infty )$ such that f(s)/s→∞$f\left(s\right)/s\to \infty$ as s→∞$s\to \infty$.     

Boundedness of solutions for Duffing-type equation

The boundedness of all solutions is shown for Duffing-type equations wherep ₁,p ₂,...,p _2n are of period 1 and of Lipschitzian continuity andp _n+1,...,p _2n are of Zygmundian continuity. This conclusion implies that the boundedness phenomenon for the Duffing-type equations does not require the smoothness in the time-variable, thus answering the question posed by Dieckerhoff and Zehnder.     

Boundedness of solutions for anisotropic degenerate elliptic equations with nonstandard growth

Under nonstandard growth conditions, following Moser's iteration technique, we prove boundedness of solutions for fourth order nonlinear elliptic equation in divergence form.     

Boundedness of solutions for nonlinear reversible system at resonance

In this paper, we are concerned with the problem of boundedness of solutions for the following nonlinear p-Laplacian:

     

Existence of quasiperiodic solutions and Littlewood’s boundedness problem of super-linear impact oscillators

So far most application of Kolmogorov-Arnold-Moser (KAM) theory has been restricted to smooth dynamical systems. In this paper, it is shown by a series of transformations that how KAM theory can be used to analyze the dynamical behavior of Duffing-type equations with impact. The analysis is carried out for the example

(0.1)     

一类局部非二次Hamilton系统的次调和解的存在性

运用极小极大方法得到一类局部非二次的Hamilton系统的次调和解的存在性定理.     

A twist condition and multiple solutions of unbounded self-adjoint operator equation with symmetries

By using the index theory for unbounded self-adjoint operator equations and the symmetric mountain pass theorem, we investigate the existence of multiple solutions for nonlinear operator equations with twist conditions. We prove an abstract theorem, and give some applications to first order Hamiltonian systems with Sturm–Liouville boundary conditions and delay differential equations.     

Invariant Tori and Boundedness in Asymmetric Oscillations

In this paper,we are concerned with the boundedness of all the solutions of the equation x″ ax^ -bx- Ф(x)=p(t),where p(t) is a smooth 2π-periodic function,a and b are positive constants,and the perturbation Ф(x) is bounded.