A Singular Initial-Value Problem for Second-Order Differential Equations
TL;DR: In this article, the existence of solutions to initial value problems for second-order nonlinear singular differential equations is proved under conditions which are considerably weaker than previously known conditions, and the existence can be explained in terms of a more simple initial value problem.
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Abstract: 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.
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References
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Ordinary differential equations
Philip Hartman
- 01 Jan 1964
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
9.4K
Ordinary Differential Equations
TL;DR: In this paper, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
5.6K
An Introduction to the Study of Stellar Structure
TL;DR: Chandrasekhar et al. as mentioned in this paper used the internal constitution of the stars to give a classical account of his own researches and of the general state of the theory at that time.
2.5K
A new algorithm for solving differential equations of Lane-Emden type
TL;DR: A reliable algorithm is employed to investigate the differential equations of Lane-Emden type using the Adomian decomposition method with an alternate framework designed to overcome the difficulty of the singular point.
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