On the Solution Spaces of Linear Second-Order Homogeneous Ordinary Differential Equations and Associated Boundary Conditions
✍ Scribed by J. Das (neé Chaudhari)
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 139 KB
- Volume
- 200
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
This note deals with linear second-order homogeneous ordinary differential equations associated with linear homogeneous boundary conditions. We find those solutions of the differential equation that satisfy a given boundary condition. Also, we determine the set of all those boundary conditions that will be satisfied by a given solution of the differential equation.
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## Abstract In this paper we deal with boundary value problems equation image where __l__ : __C__^1^([__a, b__], ℝ^__k__^) → ℝ^__k__^ × ℝ^__k__^ is continuous, __μ__ ≤ 0 and __φ__ is a Caratheodory map. We define the class __S__ of maps __l__, for which a global bifurcation theorem holds for the
A closed form solution of a second order linear homogeneous difference equation with variable coefficients is presented. As an application of this solution, Ž . we obtain expressions for cos n and sin n q 1 rsin as polynomials in cos .