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
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
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).
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.
