scholarly journals Oscillatory solutions of Emden-Fowler type differential equation

2021 ◽  
pp. 1-17
Author(s):  
Miroslav Bartusek ◽  
Zuzana Dosla ◽  
Mauro Marini
Keyword(s):  
Differential Equation ◽  
Oscillatory Solutions ◽  
Type Differential Equation

Additional spectral properties of the fourth-order Bessel-type differential equation

2005 ◽  
Vol 278 (12-13) ◽  
pp. 1538-1549 ◽  
Author(s):  
W. N. Everitt ◽  
H. Kalf ◽  
L. L. Littlejohn ◽  
C. Markett
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Spectral Properties ◽  
Type Differential Equation

scholarly journals Unexpected Solutions of the Nehari Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
A. Gritsans ◽  
F. Sadyrbaev
Keyword(s):  
Differential Equation ◽  
Multiple Solutions ◽  
Integral Functional ◽  
Characteristic Number ◽  
Nonlinear Ordinary Differential Equation ◽  
Oscillatory Solutions ◽  
Nehari Problem ◽  
Characteristic Numbers ◽  
Regular Shape ◽  
Asymmetric Shape

The Nehari characteristic numbers λn(a,b) are the minimal values of an integral functional associated with a boundary value problem (BVP) for nonlinear ordinary differential equation. In case of multiple solutions of the BVP, the problem of identifying of minimizers arises. It was observed earlier that for nonoscillatory (positive) solutions of BVP those with asymmetric shape can provide the minimal value to a functional. At the same time, an even solution with regular shape is not a minimizer. We show by constructing the example that the same phenomenon can be observed in the Nehari problem for the fifth characteristic number λn(a,b) which is associated with oscillatory solutions of BVP (namely, with those having exactly four zeros in (a,b)).

Tempering Kinetics of S45C Martensitic Steel

2006 ◽  
Vol 118 ◽  
pp. 375-380 ◽  
Author(s):  
Min Su Jung ◽  
Seok Jae Lee ◽  
Young Kook Lee
Keyword(s):  
Differential Equation ◽  
Kinetic Model ◽  
Kinetic Data ◽  
Martensitic Steel ◽  
Continuous Heating ◽  
Heating Rates ◽  
Strain Change ◽  
Type Differential Equation ◽  
Measured Strain ◽  
Kinetics Of

The strain change during the tempering of S45C martensitic steel was examined at different heating rates using a dilatometer. Tempering stages 1 and 3 corresponding to the precipitations of transition carbide and cementite were observed. Tempering kinetics at each stage was investigated from the relation between the measured strain and atomic volume change during tempering. From the tempering kinetic data, continuous heating tempering diagram was constructed and the tempering kinetic model was proposed as Zener-Hillert type differential equation.

scholarly journals A maximum principle for optimal control for a class of controlled systems

1996 ◽  
Vol 38 (2) ◽  
pp. 172-181
Author(s):  
Wensheng Xu
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Maximum Principle ◽  
Closed Loop ◽  
Point Boundary ◽  
Type Problem ◽  
Controlled Systems ◽  
Type Differential Equation ◽  
Special Case ◽  
Loop Form

AbstractApplying Ekeland's variational principle in this paper, we obtain a maximum principle for optimal control for a class of two-point boundary value controlled systems. The control domain need not be convex. For a special case, that is the so called LQ-type problem, we obtain the optimal control in the closed loop form and a corresponding Riccati type differential equation.

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