Polynomial Differential Equations with Small coefficients Export

@article{citeulike:4372650, abstract = {Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of the classes the upper bound can be improved when we consider real periodic solutions. We present a proof to a recent conjecture on the number of periodic solutions. The results are used to give upper bounds for the number of limit cycles of polynomial two-dimensional systems.}, archivePrefix = {arXiv}, author = {Alwash, M. A. M.}, citeulike-article-id = {4372650}, citeulike-linkout-0 = {http://arxiv.org/abs/0904.2756}, citeulike-linkout-1 = {http://arxiv.org/pdf/0904.2756}, day = {17}, eprint = {0904.2756}, keywords = {inequalities, limit\_cycles, univariate\_functions}, month = {Apr}, posted-at = {2009-04-21 18:00:50}, priority = {4}, title = {Polynomial Differential Equations with Small coefficients}, url = {http://arxiv.org/abs/0904.2756}, year = {2009} }

TY - JOUR ID - citeulike:4372650 L3 - citeulike-article-id:4372650 N2 - Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of the classes the upper bound can be improved when we consider real periodic solutions. We present a proof to a recent conjecture on the number of periodic solutions. The results are used to give upper bounds for the number of limit cycles of polynomial two-dimensional systems. TI - Polynomial Differential Equations with Small coefficients KW - inequalities KW - limit_cycles KW - univariate_functions AU - Alwash, MAM PY - 2009/Apr/17/ UR - http://arxiv.org/abs/0904.2756 ER -