ON THE GLOBAL SOLUTION TO THE DIFFERENTIAL EQUATION FOR THE N-POINT CONFORMAL CORRELATOR

1989 ◽  
Vol 04 (25) ◽  
pp. 2483-2486
Author(s):  
A. ROY CHOWDHURY ◽  
SWAPNA ROY
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Global Solution ◽  
Correlation Functions ◽  
Global Solutions ◽  
Second Order ◽  
Second Order Differential Equations

We have obtained compact expressions for the global solutions of the second order differential equations for the n-point conformal correlation functions. These equations were initially deduced by Belavin, Polyakov and Zamolodchikov. The monodromy property of such solutions can be ascertained from these expressions very easily.

scholarly journals Periodic solutions for periodic second-order differential equations with variable potentials

2018 ◽  
Vol 24 (2) ◽  
pp. 127-137
Author(s):  
Jaume Llibre ◽  
Ammar Makhlouf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

scholarly journals Interval oscillation criteria for certain forced second-order differential equations

2012 ◽  
Vol 28 (2) ◽  
pp. 337-344
Author(s):  
ERCAN TUNC ◽  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Half Line ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Interval Oscillation

By using generalized Riccati transformations and an inequality due to Hardy et al., several new interval oscillation criteria are established for the nonlinear damped differential equation... The new interval oscillation criteria are different from most known ones in the sense they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. Our results improve and extend the known some results in the literature.

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.

ON THE ASYMPTOTIC EXPANSIONS OF NUMERICAL SOLUTIONS TO SECOND ORDER DIFFERENTIAL EQUATIONS WITH A REGULAR SINGULAR POINT

2001 ◽  
Vol 11 (01) ◽  
pp. 163-177
Author(s):  
RICHARD WEISS ◽  
FRANK R. de HOOG ◽  
ROBERT S. ANDERSSEN
Keyword(s):  
Differential Equation ◽  
Singular Point ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Approximation ◽  
Numerical Solutions ◽  
Second Order ◽  
Regular Singular Point ◽  
Second Order Differential Equations ◽  
Uniform Asymptotic Expansion

When difference schemes with uniformly spaced gridpoints are applied to second order ordinary differential equations with a regular singular point, it is often the case that the resulting numerical approximation does not have a uniform asymptotic expansion. As a consequence, postprocessing, such as h2-extrapolation is not an option. This paper examines the cause of this phenomenon and finds that the existence of such expansions requires the discretization of the boundary conditions at the singular point to be compatible with the discretization of the differential equation. In addition, it is shown how an understanding of the need for compatible discretization can assist in the construction of schemes for several classes of equations that arise when symmetry is used to reduce partial differential equations to ordinary differential equations with a regular singular point.

scholarly journals Generalized Variational Oscillation Principles for Second-Order Differential Equations with Mixed-Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Jing Shao ◽  
Fanwei Meng ◽  
Xinqin Pang
Keyword(s):  
Differential Equation ◽  
Variational Principle ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Second Order ◽  
Generalized Variational Principle ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Mixed Nonlinearities

Using generalized variational principle and Riccati technique, new oscillation criteria are established for forced second-order differential equation with mixed nonlinearities, which improve and generalize some recent papers in the literature.

Periodic solutions of nonautonomous second-order differential equations with a p-Laplacian

Analysis ◽  
2017 ◽  
Vol 37 (1) ◽  
pp. 1-11
Author(s):  
Hairong Lian ◽  
Dongli Wang ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Periodic Solutions ◽  
Periodic Boundary ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Second Order ◽  
Periodic Boundary Value Problem ◽  
Second Order Differential Equations

AbstractIn this paper, we study a periodic boundary value problem for a nonautonomous second-order differential equation with a

scholarly journals A singular functional-differential equation

1982 ◽  
Vol 5 (3) ◽  
pp. 497-501 ◽  
Author(s):  
P. D. Siafarikas
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Existence Theorem ◽  
Functional Differential Equation ◽  
Shift Operator ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Functional Differential

The representation of the Hardy-Lebesque space by means of the shift operator is used to prove an existence theorem for a singular functional-differential equation which yields, as a corollary, the well known theory of Frobenius for second order differential equations.

The Krall Polynomials as Solutions to a Second Order Differential Equation

1983 ◽  
Vol 26 (4) ◽  
pp. 410-417 ◽  
Author(s):  
Lance L. Littlejohn
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Order Differential Equation ◽  
Order Equation ◽  
Second Order ◽  
Polynomial Solutions ◽  
Second Order Differential Equations ◽  
Image Position

AbstractA popular problem today in orthogonal polynomials is that of classifying all second order differential equations which have orthogonal polynomial solutions. We show that the Krall polynomials satisfy a second order equation of the form1.1

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