منابع مشابه
The Uniqueness Theorem for the Solutions of Dual Equations of Sturm-Liouville Problems with Singular Points and Turning Points
In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.
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We show how certain singularities of quasilinear diierential and diierential-algberaic equations can be resolved by taking the solutions to be integral manifolds of certain distributions rather than curves with speciic parametrization.
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Under appropriate assumptions, it is shown that there is a di eomorphism that transforms solutions of the implicit di erential equation
متن کاملGeneralized Helices and Singular Points
In this paper, we define X-slant helix in Euclidean 3-space and we obtain helix, slant helix, clad and g-clad helix as special case of the X-slant helix. Then we study Darboux, tangential darboux developable surfaces and their singular points. Especially we show that the striction lines of these surfaces are singular locus of the surfaces.
متن کاملA Normal Form for Implicit Differential Equations near Singular Points
| We consider di erential equations A(x) _ x = g(x), where A is an n n-matrix of C 1 functions and g is C 1 . We investigate the above di erential equation about singular points x 0 that are standard in the sense of Rabier. In particular, the null space of A(x 0 ) is of dimension 1. We show that there is a C 1 -di eomorphism that transforms the above equation about x 0 into x 1 _ x 1 = 1, _ x 2...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1953
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1953-0058859-1