1. CMB Online first
||On the limit cycles of linear differential systems with homogeneous nonlinearities|
We consider the class of polynomial differential systems of the
$\dot x= \lambda x-y+P_n(x,y)$, $\dot y=x+\lambda y+ Q_n(x,y),$ where
$P_n$ and $Q_n$ are homogeneous polynomials of degree $n$. For
class of differential systems we summarize the known results
existence of limit cycles, and we provide new results for their
nonexistence and existence.
Keywords:polynomial differential system, limit cycles, differential equations on the cylinder
2. CMB 2011 (vol 56 pp. 388)
||Application of Measure of Noncompactness to Infinite Systems of Differential Equations|
In this paper we determine the Hausdorff measure of noncompactness on
the sequence space $n(\phi)$ of W. L. C. Sargent.
Further we apply
the technique of measures of noncompactness to the theory of infinite
systems of differential equations in the Banach sequence spaces
$n(\phi)$ and $m(\phi)$. Our aim is to present some existence results
for infinite systems of differential equations formulated with the help
of measures of noncompactness.
Keywords:sequence spaces, BK spaces, measure of noncompactness, infinite system of differential equations
Categories:46B15, 46B45, 46B50, 34A34, 34G20
3. CMB 2011 (vol 55 pp. 400)
||Eisenstein Series and Modular Differential Equations|
The purpose of this paper is to solve various differential
equations having Eisenstein series as coefficients using various tools and techniques. The solutions
are given in terms of modular forms, modular functions, and
Keywords:differential equations, modular forms, Schwarz derivative, equivariant forms
4. CMB 2010 (vol 53 pp. 475)
||Nonlinear Multipoint Boundary Value Problems for Second Order Differential Equations|
In this paper we shall discuss nonlinear multipoint boundary value problems for second order differential equations when deviating arguments depend on the unknown solution. Sufficient conditions under which such problems have extremal and quasi-solutions are given. The problem of when a unique solution exists is also investigated. To obtain existence results, a monotone iterative technique is used. Two examples are added to verify theoretical results.
Keywords:second order differential equations, deviated arguments, nonlinear boundary conditions, extremal solutions, quasi-solutions, unique solution
5. CMB 2010 (vol 53 pp. 367)