Conjugacy of half-linear second-order differential equations

2000 ◽  
Vol 130 (3) ◽  
pp. 517-525 ◽  
Author(s):  
Ondřej Došlý ◽  
Árpád Elbert
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Focal Point ◽  
Second Order ◽  
Oscillation Criterion ◽  
Riccati Transformation ◽  
Second Order Differential Equations ◽  
Generalized Riccati Transformation ◽  
Image Position

Focal point and conjugacy criteria for the half-linear second-order differential equation are obtained using the generalized Riccati transformation. An oscillation criterion is given in case when the function c(t) is periodic.

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.

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

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 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

Nonprincipal solutions in oscillation criteria for half-linear differential equations

2010 ◽  
Vol 47 (1) ◽  
pp. 127-137
Author(s):  
Ondřej Došlý ◽  
Jana Řezníčková
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Second Order ◽  
Oscillation Criterion ◽  
Linear Differential Equations ◽  
Integral Term ◽  
Oscillation Criteria ◽  
Second Order Differential Equation ◽  
Linear Differential

We establish a new oscillation criterion for the half-linear second order differential equation \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$(r(t)\Phi (x'))' + c(t)\Phi (x) = 0,\Phi (x): = |x|^{p - 2} x,p > 1.$$ \end{document} In this criterion, an integral term appears which involves a nonprincipal solution of a certain equation associated with (*).

scholarly journals Asymptotic integration of the second order differential equation, resonance effect

2015 ◽  
Vol 63 (1) ◽  
pp. 223-235
Author(s):  
Barbara Pietruczuk
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Resonance Effect ◽  
Second Order ◽  
Asymptotic Integration ◽  
Asymptotic Formulas ◽  
Von Neumann ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation

Abstract There will be presented asymptotic formulas for solutions of the equation y'' + (1 + φ (x))y = 0, 0 < x0 < x < ∞ , where function is small in a certain sense for large values of the argument. Usage of method of L-diagonal systems allows to obtain various forms of solutions depending on the properties of function φ . The main aim will be discussion about the second order differential equations possesing a resonance effect known for Wigner von Neumann potential. A class of potentials generalizing that of Wigner von Neumann will be presented.

scholarly journals On a second order differential equation with piecewise constant mixed arguments

2011 ◽  
Vol 27 (1) ◽  
pp. 1-12
Author(s):  
H. BEREKETOGLU ◽  
◽  
G. SEYHAN ◽  
F. KARAKOC ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Order Differential Equation ◽  
Zero Solution ◽  
Second Order ◽  
Uniqueness Of Solutions ◽  
Piecewise Constant ◽  
Second Order Differential Equations ◽  
Mixed Arguments

We prove the existence and uniqueness of solutions of a class of second order differential equations with piecewise constant mixed arguments and we show that the zero solution of Eq. (1.1) is a global attractor. Also, we study some properties of solutions of Eq. (1.1) such as oscillation, nonoscillation, and periodicity.

scholarly journals Local convexity for second order differential equations on a Lie algebroid

2021 ◽  
Vol 13 (3) ◽  
pp. 477
Author(s):  
Juan Carlos Marrero ◽  
David Martín de Diego ◽  
Eduardo Martínez
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Second Order ◽  
Lie Algebroid ◽  
Local Convexity ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation

<p style='text-indent:20px;'>A theory of local convexity for a second order differential equation (${\text{sode}}$) on a Lie algebroid is developed. The particular case when the ${\text{sode}}$ is homogeneous quadratic is extensively discussed.</p>

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

Sign in / Sign up

Export Citation Format

Share Document