scholarly journals A singular initial value problem for second and third order differential equations

1995 ◽  
Vol 68 (2) ◽  
pp. 249-257 ◽  
Author(s):  
Wojciech Mydlarczyk
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Initial Value ◽  
Third Order ◽  
Singular Initial Value Problem

scholarly journals A singular initial value problem for some functional differential equations

2004 ◽  
Vol 2004 (3) ◽  
pp. 261-270 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan ◽  
Oleksandr E. Zernov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Asymptotic Properties ◽  
Functional Differential Equations ◽  
Initial Value ◽  
Singular Initial Value Problem ◽  
Functional Differential

For the initial value problem trx′(t)=at+b1x(t)+b2x(q1t)+b3trx′(q2t)+φ(t,x(t),x(q1t),x′(t),x′(q2t)), x(0)=0, where r>1, 0<qi≤1, i∈{1,2}, we find a nonempty set of continuously differentiable solutions x:(0,ρ]→ℝ, each of which possesses nice asymptotic properties when t→+0.

scholarly journals Singular Initial Value Problem for Certain Classes of Systems of Ordinary Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Josef Diblík ◽  
Josef Rebenda ◽  
Zdeněk Šmarda
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problem ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
Singular Initial Value Problem ◽  
The Right

The paper is devoted to the study of the solvability of a singular initial value problem for systems of ordinary differential equations. The main results give sufficient conditions for the existence of solutions in the right-hand neighbourhood of a singular point. In addition, the dimension of the set of initial data generating such solutions is estimated. An asymptotic behavior of solutions is determined as well and relevant asymptotic formulas are derived. The method of functions defined implicitly and the topological method (Ważewski's method) are used in the proofs. The results generalize some previous ones on singular initial value problems for differential equations.

scholarly journals A Singular Initial-Value Problem for Second-Order Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Afgan Aslanov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Existence Of Solutions ◽  
Local Existence ◽  
Second Order ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Existence Of A Solution ◽  
Local Existence And Uniqueness ◽  
Singular Initial Value Problem

We are interested in the existence of solutions to initial-value problems for second-order nonlinear singular differential equations. We show that the existence of a solution can be explained in terms of a more simple initial-value problem. Local existence and uniqueness of solutions are proven under conditions which are considerably weaker than previously known conditions.

scholarly journals Geometric Properties Solutions of a Class of Third-Order Linear Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
Afaf Ali Abubaker ◽  
Maslina Darus
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Linear Differential Equations ◽  
Open Unit ◽  
Open Unit Disk ◽  
Initial Value ◽  
Third Order ◽  
Geometric Properties ◽  
Order Linear ◽  
Linear Differential

We aim at investigating the geometric properties of the solutions of the initial-value problem which involves the following third-order linear differential equations: ω′′′(z)+Q(z)ω′(z)=0, ω(0)=0, ω′(0)=1, ω′′(0)=0, where Q(z) is analytic in the open unit disk U.

scholarly journals Crystalline flow starting from a general polygon

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mi-Ho Giga ◽  
Yoshikazu Giga ◽  
Ryo Kuroda ◽  
Yusuke Ochiai
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problem ◽  
Initial Value ◽  
Singular Initial Value Problem ◽  
Self Similar

<p style='text-indent:20px;'>This paper solves a singular initial value problem for a system of ordinary differential equations describing a polygonal flow called a crystalline flow. Such a problem corresponds to a crystalline flow starting from a general polygon not necessarily admissible in the sense that the corresponding initial value problem is singular. To solve the problem, a self-similar expanding solution constructed by the first two authors with H. Hontani (2006) is effectively used.</p>

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