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Search: All articles in the CMB digital archive with keyword differential equations

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1. CMB 2015 (vol 58 pp. 818)

Llibre, Jaume; Zhang, Xiang
 On the Limit Cycles of Linear Differential Systems with Homogeneous Nonlinearities We consider the class of polynomial differential systems of the form $\dot x= \lambda x-y+P_n(x,y)$, $\dot y=x+\lambda y+ Q_n(x,y),$ where $P_n$ and $Q_n$ are homogeneous polynomials of degree $n$. For this class of differential systems we summarize the known results for the existence of limit cycles, and we provide new results for their nonexistence and existence. Keywords:polynomial differential system, limit cycles, differential equations on the cylinderCategories:34C35, 34D30

2. CMB 2011 (vol 56 pp. 388)

Mursaleen, M.
 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 equationsCategories:46B15, 46B45, 46B50, 34A34, 34G20

3. CMB 2011 (vol 55 pp. 400)

Sebbar, Abdellah; Sebbar, Ahmed
 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 equivariant forms. Keywords:differential equations, modular forms, Schwarz derivative, equivariant formsCategories:11F11, 34M05

4. CMB 2010 (vol 53 pp. 475)

Jankowski, Tadeusz
 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 solutionCategories:34A45, 34K10

5. CMB 2010 (vol 53 pp. 367)

Stamov, Gani Tr.
 Almost Periodicity and Lyapunov's Functions for Impulsive Functional Differential Equations with Infinite Delays This paper studies the existence and uniqueness of almost periodic solutions of nonlinear impulsive functional differential equations with infinite delay. The results obtained are based on the Lyapunov--Razumikhin method and on differential inequalities for piecewise continuous functions. Keywords:almost periodic solutions, impulsive functional differential equationsCategories:34K45, 34B37
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