On the limit point classification of second order differential equations

1973 ◽  
Vol 132 (4) ◽  
pp. 297-304 ◽  
Author(s):  
James S. W. Wong ◽  
Anton Zettl
Keyword(s):  
Differential Equations ◽  
Limit Point ◽  
Second Order ◽  
Second Order Differential Equations

Nonclassical Orthogonal Polynomials as Solutions to Second Order Differential Equations

1982 ◽  
Vol 25 (3) ◽  
pp. 291-295 ◽  
Author(s):  
Lance L. Littlejohn ◽  
Samuel D. Shore
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Order Differential Equation ◽  
Order Equation ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Image Position

AbstractOne of the more popular problems today in the area of orthogonal polynomials is the classification of all orthogonal polynomial solutions to the second order differential equation:In this paper, we show that the Laguerre type and Jacobi type polynomials satisfy such a second order equation.

scholarly journals Existence and Uniqueness of Homoclinic Solution for a Class of Nonlinear Second-Order Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Lijuan Chen ◽  
Shiping Lu
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Homoclinic Orbit ◽  
Limit Point ◽  
Existence And Uniqueness ◽  
Homoclinic Solution ◽  
Second Order ◽  
Continuation Theorem ◽  
Mawhin’S Continuation Theorem ◽  
Second Order Differential Equations

The authors study the existence and uniqueness of a set with2kT-periodic solutions for a class of second-order differential equations by using Mawhin's continuation theorem and some analysis methods, and then a unique homoclinic orbit is obtained as a limit point of the above set of2kT-periodic solutions.

scholarly journals ON THE CLASSIFICATION OF SINGULAR AUTOMORPHIC DIFFERENTIAL EQUATIONS AND FLOW S ON THE RIEMANN SPHERE

1995 ◽  
Vol 26 (1) ◽  
pp. 13-19
Author(s):  
K. F. KUIKEN ◽  
J. T. MASTERSON
Keyword(s):  
Differential Equations ◽  
Riemann Sphere ◽  
Fluid Flows ◽  
Second Order ◽  
Singular Points ◽  
Conic Sections ◽  
Countable Number ◽  
Second Order Differential Equations

In this paper, parameterizations are constructed for spaces of automor­ phic second order differential equations on certam subsets of $\hat C$. These equations have coefficients with a countable number of regular singular points on fundamen­ tal domains for bimeromorphic deformations of Kleiman groups. The equations considered are generalizations of classically-considered equations, including the hy­ pergeometric and Heun's equations, or have singular points on fam1hes of curves, including lines, conic sections, Joukowski airfoils or biconformal images of these curves. Global fluid flows associate with these equations are constructed and classified.

scholarly journals Limit Circle/Limit Point Criteria for Second-Order Sublinear Differential Equations with Damping Term

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Jing Shao ◽  
Wei Song
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Limit Point ◽  
Second Order ◽  
Damping Term ◽  
Limit Circle ◽  
New Criteria ◽  
Point Type ◽  
Circle Limit

The purpose of the present paper is to establish some new criteria for the classification of the sublinear differential equation as of the nonlinear limit circle type or of the nonlinear limit point type. The criteria presented here generalize some known results in the literature.

20.—On the Limit-point and Limit-circle Theory of Second-order Differential Equations

1975 ◽  
Vol 72 (3) ◽  
pp. 245-256
Author(s):  
K. S. Ong
Keyword(s):  
Differential Equations ◽  
Weight Function ◽  
Limit Point ◽  
Circle Method ◽  
Second Order ◽  
Limit Circle ◽  
Second Order Differential Equations

SynopsisIn this paper the Weyl limit-point and limit-circle theory of second-order differential equations is extended to the case that the weight function is allowed to take on both positive and negative values—the polar case. This extension is achieved using Weyl's limit circle method.

Banach Lie Algebroids

2011 ◽  
Vol 57 (2) ◽  
pp. 409-416
Author(s):  
Mihai Anastasiei
Keyword(s):  
Differential Equations ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Second Order ◽  
Lie Algebroids ◽  
Second Order Differential Equations

Banach Lie AlgebroidsFirst, we extend the notion of second order differential equations (SODE) on a smooth manifold to anchored Banach vector bundles. Then we define the Banach Lie algebroids as Lie algebroids structures modeled on anchored Banach vector bundles and prove that they form a category.

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