scholarly journals Certain second-order differential inequality of neutral type

2000 ◽  
Vol 13 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Peiguang Wang ◽  
Weigao Ge
Keyword(s):  
Differential Inequality ◽  
Neutral Type ◽  
Second Order

scholarly journals Further results on differential inequality of a class of second order neutral type

2004 ◽  
Vol 35 (1) ◽  
pp. 43-52 ◽  
Author(s):  
Peiguang Wang ◽  
Yonghong Wu
Keyword(s):  
Positive Solutions ◽  
Differential Inequality ◽  
Neutral Type ◽  
Second Order ◽  
Differential Inequalities ◽  
Deviating Arguments ◽  
Distributed Deviating Arguments ◽  
Existing Result

In this paper, we develop several new results related to the nonexistence criteria for eventually positive solutions of a class of second order neutral differential inequalities with distributed deviating arguments. The work generalizes various existing result.

scholarly journals Oscillation criteria for second-order nonlinear delay dynamic equations of neutral type

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Ming Zhang ◽  
Wei Chen ◽  
MMA El-Sheikh ◽  
RA Sallam ◽  
AM Hassan ◽  
...  
Keyword(s):  
Neutral Type ◽  
Second Order ◽  
Dynamic Equations ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations ◽  
Nonlinear Delay

scholarly journals Some New Oscillation Results for Fourth-Order Neutral Differential Equations with a Canonical Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Omar Bazighifan
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Differential Inequality ◽  
Order Differential Equation ◽  
Neutral Type ◽  
Comparison Method ◽  
Oscillatory Behaviour ◽  
Neutral Differential Equations ◽  
First Order ◽  
Equation Of Neutral Type

By this work, our aim is to study oscillatory behaviour of solutions to 4th-order differential equation of neutral type L y ′ + ∑ j = 1 k q j y z β g j y = 0 where L y = ξ y w ‴ y α , w y : = z y + r y z g ˜ y . By using the comparison method with first-order differential inequality, we find new oscillation conditions for this equation.

XXIII.—On an Extension to an Integro-differential Inequality of Hardy, Littlewood and Polya

1972 ◽  
Vol 69 (4) ◽  
pp. 295-333 ◽  
Author(s):  
W. N. Everitt
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Differential Inequality ◽  
Order Differential Equation ◽  
Order Equation ◽  
Second Order ◽  
Image Position ◽  
Fourth Order Differential Equation

SynopsisThis paper considers an extension of the following inequality given in the book Inequalities by Hardy, Littlewood and Polya; let f be real-valued, twice differentiable on [0, ∞) and such that f and f are both in the space fn, ∞), then f′ is in L,2(0, ∞) andThe extension consists in replacing f′ by M[f] wherechoosing f so that f and M[f] are in L2(0, ∞) and then seeking to determine if there is an inequality of the formwhere K is a positive number independent of f.The analysis involves a fourth-order differential equation and the second-order equation associated with M.A number of examples are discussed to illustrate the theorems obtained and to show that the extended inequality (*) may or may not hold.

scholarly journals Spatial Behavior of a Coupled System of Wave-Plate Type

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Gusheng Tang ◽  
Yan Liu ◽  
Wenhui Liao
Keyword(s):  
Differential Inequality ◽  
Coupled System ◽  
Second Order ◽  
Spatial Behavior ◽  
Decay Estimates ◽  
Spatial Decay ◽  
Area Measure ◽  
First Order ◽  
Wave Plate ◽  
Plate Type

The spatial behavior of a coupled system of wave-plate type is studied. We get the alternative results of Phragmén-Lindelöf type in terms of an area measure of the amplitude in question based on a first-order differential inequality. We also get the spatial decay estimates based on a second-order differential inequality.

On an inequality of the Kolmogorov type for a second-order differential expression

1993 ◽  
Vol 442 (1916) ◽  
pp. 555-569 ◽  
Keyword(s):  
Differential Expression ◽  
Differential Inequality ◽  
Second Order ◽  
Numerical Treatment ◽  
Kolmogorov Type ◽  
Best Constant

In this paper we discuss an integro-differential inequality formed from the square of a second-order differential expression. A connection between the existence of the inequality and the Titchmarsh–Weyl m -function is established and it is shown that the best constant in the inequality is determined by the behaviour of the m -function. Analytic results are established for specific classes of problems. A numerical treatment of the inequality is also discussed and estimates of the best constant in specific examples are given.

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