In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the...In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.展开更多
In this paper, we consider the electromagnetic scattering by a periodic chiral structure. The media is homogeneous and the structure is periodic in one direction and invariant in another direction. The electromagnetic...In this paper, we consider the electromagnetic scattering by a periodic chiral structure. The media is homogeneous and the structure is periodic in one direction and invariant in another direction. The electromagnetic fields inside the chiral medium are governed by Maxwell equations together with the Drude-BornFedorov equations. We simplify the problem to a two-dimensional scattering problem and discuss the existence and the uniqueness of solutions by an integral equation approach. We show that for all but possibly a discrete set of wave numbers, the integral equation has a unique solution.展开更多
We prove the existence of quasiperiodic solutions and Lagrange stability for a class of differential equations with jumping nonlinearity x+ax^+-bx^-+φ(x)=p(t), where a, b】0, p(t)∈ C(R/2πZ) and φ: R→R is an unbou...We prove the existence of quasiperiodic solutions and Lagrange stability for a class of differential equations with jumping nonlinearity x+ax^+-bx^-+φ(x)=p(t), where a, b】0, p(t)∈ C(R/2πZ) and φ: R→R is an unbounded function.展开更多
This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in ...This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in x and even in t, which are 1-periodic in t, and the function g satisfies g(x,t/x+, as|x| - +. Using the KAM theory for reversible systems, the author proves the existence of invariant tori and thus the boundedness of all the solutions and the existence of quasiperiodic solutions and subharmonic solutions.展开更多
文摘In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.
基金The Special Funds for Major State Basic Research Projects (G1999032802) in China and the NNSF (10076006) of China.
文摘In this paper, we consider the electromagnetic scattering by a periodic chiral structure. The media is homogeneous and the structure is periodic in one direction and invariant in another direction. The electromagnetic fields inside the chiral medium are governed by Maxwell equations together with the Drude-BornFedorov equations. We simplify the problem to a two-dimensional scattering problem and discuss the existence and the uniqueness of solutions by an integral equation approach. We show that for all but possibly a discrete set of wave numbers, the integral equation has a unique solution.
基金Supported by the National Natural Science Foundation of China
文摘We prove the existence of quasiperiodic solutions and Lagrange stability for a class of differential equations with jumping nonlinearity x+ax^+-bx^-+φ(x)=p(t), where a, b】0, p(t)∈ C(R/2πZ) and φ: R→R is an unbounded function.
文摘This paper is concerned with the boundedness of solutions for second order differential equations x + f(x, t)x + g(x, t) = 0, which are neither dissipative nor conservative, and where the functions f and g are odd in x and even in t, which are 1-periodic in t, and the function g satisfies g(x,t/x+, as|x| - +. Using the KAM theory for reversible systems, the author proves the existence of invariant tori and thus the boundedness of all the solutions and the existence of quasiperiodic solutions and subharmonic solutions.
