Fix a collection of polynomial vector fields on R3with a singularity at the origin,for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue. Some such systems admit a loc...Fix a collection of polynomial vector fields on R3with a singularity at the origin,for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue. Some such systems admit a local analytic first integral,which then defines a local center manifold of the system. Conditions for existence of a first integral are given by the vanishing certain polynomial or rational functions in the coefficients of the system called focus quantities. In this paper we prove that the focus quantities have a structure analogous to that in the two-dimensional case and use it to formulate an efficient algorithm for computing them.展开更多
We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class...We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class of rational differential systems with a cubic polynomial as its numerator.展开更多
We prove several new comparison results and develop the monotone iterative technique to show the existence of extremal solutions to a kind of periodic boundary value problem (PBVP) for nonlinear integro-differential e...We prove several new comparison results and develop the monotone iterative technique to show the existence of extremal solutions to a kind of periodic boundary value problem (PBVP) for nonlinear integro-differential equation of mixed type on time scales.展开更多
基金VR acknowledges the support of this work by the Slovenian Research Agency and by a Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme,FP7-PEOPLE-2012-IRSES-316338
文摘Fix a collection of polynomial vector fields on R3with a singularity at the origin,for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue. Some such systems admit a local analytic first integral,which then defines a local center manifold of the system. Conditions for existence of a first integral are given by the vanishing certain polynomial or rational functions in the coefficients of the system called focus quantities. In this paper we prove that the focus quantities have a structure analogous to that in the two-dimensional case and use it to formulate an efficient algorithm for computing them.
基金supported by the National Natural Science Foundation of China (10961011)the Slovene Human Resources and Scholarship Fundthe Slovenian Research Agency, by the Nova Kreditna Banka Maribor, by TELEKOM Slovenije and by the Transnational Access Programme at RISC-Linz of the European Commission Framework 6 Programme for Integrated Infrastructures Initiatives under the project SCIEnce (Contract No. 026133)
文摘We describe an approach to studying the center problem and local bifurcations of critical periods at infinity for a class of differential systems. We then solve the problem and investigate the bifurcations for a class of rational differential systems with a cubic polynomial as its numerator.
基金supported by Shanghai Normal University Leading Academic Discipline Project DZL805National Natural Science Foundation of China (10671127)National Natural Science Foundation of Shanghai (08ZR1416000), Ad futura scientific and educational foundation of the Republic of Slovenia, the Ministry of Higher Education, Science and Technology of the Republic of Slovenia, by the Nova Kreditna Banka Maribor and by TELEKOM Slovenije
文摘We prove several new comparison results and develop the monotone iterative technique to show the existence of extremal solutions to a kind of periodic boundary value problem (PBVP) for nonlinear integro-differential equation of mixed type on time scales.
