Chapter 9: First-Order Hyperbolic PDEs and Delay Equations

2008 ◽  
pp. 109-114
Keyword(s):  
Delay Equations ◽  
Hyperbolic Pdes ◽  
First Order

Backstepping Boundary Control for First-Order Hyperbolic PDEs on Inverted Pendulum Stabilization with Constant Input Delay

2021 ◽  
Author(s):  
Arnab Pal ◽  
Ramashis Banerjee ◽  
Debottam Mukherjee ◽  
Samrat Chakraborty ◽  
Pabitra Kumar Guchhait ◽  
...  
Keyword(s):  
Boundary Control ◽  
Inverted Pendulum ◽  
Input Delay ◽  
Constant Input ◽  
Hyperbolic Pdes ◽  
First Order

scholarly journals Improved Approach for Studying Oscillatory Properties of Fourth-Order Advanced Differential Equations with p-Laplacian Like Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 656 ◽  
Author(s):  
Omar Bazighifan ◽  
Thabet Abdeljawad
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Equations ◽  
Riccati Transformation ◽  
Oscillation Criteria ◽  
First Order ◽  
Oscillatory Properties

This paper aims to study the oscillatory properties of fourth-order advanced differential equations with p-Laplacian like operator. By using the technique of Riccati transformation and the theory of comparison with first-order delay equations, we will establish some new oscillation criteria for this equation. Some examples are considered to illustrate the main results.

scholarly journals New criteria for oscillation of nonlinear neutral differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Osama Moaaz
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Delay Equations ◽  
Neutral Differential Equation ◽  
Neutral Differential Equations ◽  
First Order ◽  
Riccati Substitution ◽  
Gamma S ◽  
New Criteria

AbstractThe aim of this work is to offer sufficient conditions for the oscillation of neutral differential equation second order $$ \bigl( r ( t ) \bigl[ \bigl( y ( t ) +p ( t ) y \bigl( \tau ( t ) \bigr) \bigr) ^{\prime } \bigr] ^{\gamma } \bigr) ^{\prime }+f \bigl( t,y \bigl( \sigma ( t ) \bigr) \bigr) =0, $$(r(t)[(y(t)+p(t)y(τ(t)))′]γ)′+f(t,y(σ(t)))=0, where $\int ^{\infty }r^{-1/\gamma } ( s ) \,\mathrm{d}s= \infty $∫∞r−1/γ(s)ds=∞. Based on the comparison with first order delay equations and by employ the Riccati substitution technique, we improve and complement a number of well-known results. Some examples are provided to show the importance of these results.

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