ﻻ يوجد ملخص باللغة العربية
In this paper, I have proved that for a class of polynomial differential systems of degree n+1 ( where n is an arbitrary positive integer) the composition conjecture is true. I give the sufficient and necessary conditions for these differential systems to have a center at origin point by using a different method from the previous references. By this I can obtain all the focal values of these systems for an arbitrary n and their expressions are succinct and beautiful. I believe that the idea and method of this article can be used to solve the center-focus problem of more high-order polynomial differential systems.
In this paper, we give a direct method to study the isochronous centers on center manifolds of three dimensional polynomial differential systems. Firstly, the isochronous constants of the three dimensional system are defined and its recursive formula
A class of two-dimensional linear differential systems is considered. The box-counting dimension of the graphs of solution curves is calculated. Criteria to obtain the box-counting dimension of spirals are also established.
In this, paper, we give a complete system of analytic invariants for the unfoldings of nonresonant linear differential systems with an irregular singularity of Poincare rank 1 at the origin over a fixed neighborhood $D_r$. The unfolding parameter $ep
The paper is a comprehensive study of the $L_p$ and the Schauder estimates for higher-order divergence type parabolic systems with discontinuous coefficients in the half space and cylindrical domains with conormal derivative boundary condition. For t
In the present paper, we study the number of zeros of the first order Melnikov function for piecewise smooth polynomial differential system, to estimate the number of limit cycles bifurcated from the period annulus of quadratic isochronous centers, w