Analytic Invariant Curves for an Iterative Equation Related to Ricker-type Second-order Equation

2021 ◽  
Vol 37 (7) ◽  
pp. 1041-1052
Author(s):  
Hou Yu Zhao ◽  
Michal Fečkan
Keyword(s):  
Order Equation ◽  
Second Order ◽  
Invariant Curves ◽  
Iterative Equation ◽  
Analytic Invariant

scholarly journals Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 285
Author(s):  
Saad Althobati ◽  
Jehad Alzabut ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Order Equation ◽  
Second Order ◽  
Riccati Technique ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Main Equation ◽  
Non Linear ◽  
Even Order

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

scholarly journals A relativistic basis of the quantum theory.—II

1934 ◽  
Vol 145 (855) ◽  
pp. 645-656 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Wave Equation ◽  
Quantum Theory ◽  
General Expression ◽  
Matrix Equation ◽  
Covariant Derivative ◽  
Riemannian Geometry ◽  
Order Equation ◽  
Second Order ◽  
Space Curvature

The paper is a continuation of the last paper communicated to these 'Proceedings.' In that paper, which we shall refer to as the first paper, a more general expression for space curvature was obtained than that which occurs in Riemannian geometry, by a modification of the Riemannian covariant derivative and by the use of a fifth co-ordinate. By means of a particular substitution (∆ μσ σ = 1/ψ ∂ψ/∂x μ ) it was shown that this curvature takes the form of the second order equation of quantum mechanics. It is not a matrix equation, however but one which has the character of the wave equation as it occurred in the earlier form of the quantum theory. But it contains additional terms, all of which can be readily accounted for in physics, expect on which suggested an identification with energy of the spin.

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