On a codimension 3 bifurcation of plane vector fields with symmetry
On a maximal number of period annuli.
On algebraic approach in quadratic systems.
On algebraic solutions of algebraic Pfaff equations
We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system . We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.
On centers of cubic systems
On centers of type of polynomial systems
On first integrals for polynomial differential equations on the line
We show that any equation dy/dx = P(x,y) with P a polynomial has a global (on ℝ²) smooth first integral nonconstant on any open domain. We also present an example of an equation without an analytic primitive first integral.
On functions describing a distribution of zeros of solutions of an iterated linear differential equation of the fourth order
On holomorphic foliations without algebraic solutions.
On plane polynomial vector fields and the Poincaré problem.
On solutions of the Lagerstrom equation
On the approximation of the limit cycles function.
On the center of the generalized Liénard system
In this paper, we discuss the conditions for a center for the generalized Liénard system or with , , , , , , and for . By using a different technique, that is, by introducing auxiliary systems and using the differential inquality theorem, we are able to generalize and improve some results in [1], [2].
On the composition conjectures.
On the existence of equilibrium points, boundedness, oscillating behavior and positivity of a SVEIRS epidemic model under constant and impulsive vaccination.
On the focal points of solutions of a certain fourth order differential equation
On the limit cycle of the Liénard equation
In the paper, we give an existence theorem of periodic solution for Liénard equation , . As a result, we estimate the amplitude (maximal -value) of the limit cycle of the van der Pol equation , from above by for every . The result is an improvement of the author’s previous estimation .
On the limit cycle of the van der Pol equation
On the Limit-Point and Strong Limit-Point Classification of 2 n-th Order Differential Expressions with Widly Oscillating Coefficients.
On the number of limit cycles in perturbations of a two dimensional nonlinear differential system.