Time-delay effects on the dynamics of Li^nard type equation with one fast variable and one slow variable are investigated in the present paper. By using the methods of stability switch and geometric singular perturbat...Time-delay effects on the dynamics of Li^nard type equation with one fast variable and one slow variable are investigated in the present paper. By using the methods of stability switch and geometric singular perturbation, time-delay-induced complex oscillations and bursting are investigated, and in several case studies, the mechanism of the generation of the complex oscillations and bursting is illuminated. Numerical results demonstrate the validity of the theoretical results.展开更多
In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is t...In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is transformed to discrete system of equations, and then we obtain the solvable conditions and the explicit solutions in class L2[-π, π].展开更多
By applying the topological degree theory, we establish some sufficientconditions for the existence on T-periodic solutions for the Liénard-type equation x' + Σ from i=1to n of h_i(x)|x'|^(2α_i) + f_1(x...By applying the topological degree theory, we establish some sufficientconditions for the existence on T-periodic solutions for the Liénard-type equation x' + Σ from i=1to n of h_i(x)|x'|^(2α_i) + f_1(x)|x'|~2 + f_2(x)x' + g(t,x) = p(t). Our results extend andimprove some known results in the literature.展开更多
In this paper, we investigate the nonexistence of periodic solutions for Lienardtype equationSome brief and practical sufficient conditions on the nonexistence of periodic solutions aregiven. Our results can be easily...In this paper, we investigate the nonexistence of periodic solutions for Lienardtype equationSome brief and practical sufficient conditions on the nonexistence of periodic solutions aregiven. Our results can be easily applied to the well-known Lienard equation x+f(x) x +g(x) =0, and substantially extend and improve some known results.展开更多
In this paper, we consider the retarded Lienard-type equationwhere h is a nonnegative constant, f_1 , f_2, and g are continuous functions on R.Using Liapunov functional method, we obtain the sufficient conditions to ...In this paper, we consider the retarded Lienard-type equationwhere h is a nonnegative constant, f_1 , f_2, and g are continuous functions on R.Using Liapunov functional method, we obtain the sufficient conditions to ensurethe stability and boundedness of solutions for Eq.(1).展开更多
.In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of....In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary.We show the existence of at least one,two or infinitely many non-trivial weak solutions according to hypotheses on given functions.展开更多
The numerical mode of nonlinear wave transformation based on both the Laplace equation for water field and the Bernoulli equation for water surface is a kind of time-domain boundary problem with initial conditions. An...The numerical mode of nonlinear wave transformation based on both the Laplace equation for water field and the Bernoulli equation for water surface is a kind of time-domain boundary problem with initial conditions. And the basis for establishing the numerical mode of nonlinear wave in time domain is to trace the position of wave free surface and to calculate the instantaneous surface height and surface potential function. This paper firstly utilizes the ‘0-1' combined BEM to separate the boundary by means of discretization of Green's integral equation based on the Laplace equation, then separates the free surface of wave with FEM and derives the FEM equation of wave surface that satisfies the nonlinear boundary conditions. By jointly solving the above BEM and FEM equations, the wave potential and surface height could be obtained with iteration in time domain. Thus a new kind of nonlinear numerical mode is established for calculating wave transformation. The wave test in the numerical wave tank shows that the numerical simulation with this mode is of high accuracy.展开更多
SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equ...SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equation. The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface. The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step. In m-time iteration within the computational process of time step （n-1）At to nat, the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration. Thus, an improved tracking mode of nonlinear wave surface is estabIished, and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.展开更多
基金supported by the National Natural Science Foundation of China(11102078 and 11032009)Foundation of Jiangxi Education Committee of China(GJJ1169)
文摘Time-delay effects on the dynamics of Li^nard type equation with one fast variable and one slow variable are investigated in the present paper. By using the methods of stability switch and geometric singular perturbation, time-delay-induced complex oscillations and bursting are investigated, and in several case studies, the mechanism of the generation of the complex oscillations and bursting is illuminated. Numerical results demonstrate the validity of the theoretical results.
基金Supported by the Qufu Normal University Youth Fund(XJ201218)
文摘In this paper, we propose and discuss a class of singular integral equation of convolution type with csc(τ- θ) kernel in class L2[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is transformed to discrete system of equations, and then we obtain the solvable conditions and the explicit solutions in class L2[-π, π].
基金Supported by the National Natural Science Foundation of China (No. 10371034)the Doctor Program Foundation of the Ministry of Education of China (20010532002)Key Object of Chinese Ministry of Education ([2002] 78).
文摘By applying the topological degree theory, we establish some sufficientconditions for the existence on T-periodic solutions for the Liénard-type equation x' + Σ from i=1to n of h_i(x)|x'|^(2α_i) + f_1(x)|x'|~2 + f_2(x)x' + g(t,x) = p(t). Our results extend andimprove some known results in the literature.
文摘In this paper, we investigate the nonexistence of periodic solutions for Lienardtype equationSome brief and practical sufficient conditions on the nonexistence of periodic solutions aregiven. Our results can be easily applied to the well-known Lienard equation x+f(x) x +g(x) =0, and substantially extend and improve some known results.
文摘In this paper, we consider the retarded Lienard-type equationwhere h is a nonnegative constant, f_1 , f_2, and g are continuous functions on R.Using Liapunov functional method, we obtain the sufficient conditions to ensurethe stability and boundedness of solutions for Eq.(1).
文摘.In this paper,we consider a mixed boundary value problem for the stationary Kirchhoff-type equation containing p(-)-Laplacian.More precisely,we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary.We show the existence of at least one,two or infinitely many non-trivial weak solutions according to hypotheses on given functions.
文摘The numerical mode of nonlinear wave transformation based on both the Laplace equation for water field and the Bernoulli equation for water surface is a kind of time-domain boundary problem with initial conditions. And the basis for establishing the numerical mode of nonlinear wave in time domain is to trace the position of wave free surface and to calculate the instantaneous surface height and surface potential function. This paper firstly utilizes the ‘0-1' combined BEM to separate the boundary by means of discretization of Green's integral equation based on the Laplace equation, then separates the free surface of wave with FEM and derives the FEM equation of wave surface that satisfies the nonlinear boundary conditions. By jointly solving the above BEM and FEM equations, the wave potential and surface height could be obtained with iteration in time domain. Thus a new kind of nonlinear numerical mode is established for calculating wave transformation. The wave test in the numerical wave tank shows that the numerical simulation with this mode is of high accuracy.
基金supported by the National Natural Science Foundation of China (Grant No. 50921001)
文摘SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equation. The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface. The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step. In m-time iteration within the computational process of time step （n-1）At to nat, the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration. Thus, an improved tracking mode of nonlinear wave surface is estabIished, and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.
