scholarly journals Asymptotic properties of third-order differential equations with deviating argument

1994 ◽  
Vol 44 (1) ◽  
pp. 163-172
Author(s):  
Jozef Džurina
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Third Order ◽  
Deviating Argument

On solutions of third order nonlinear differential equations

2006 ◽  
Vol 4 (1) ◽  
pp. 46-63 ◽  
Author(s):  
Ivan Mojsej ◽  
Ján Ohriska
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Property A ◽  
Comparison Result ◽  
Third Order ◽  
Deviating Arguments ◽  
Deviating Argument ◽  
The Third

AbstractThe aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity f are related to its behavior only in a neighbourhood of zero and/or of infinity.

scholarly journals Oscillation and Asymptotic Properties of Differential Equations of Third-Order

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 192
Author(s):  
R. Elayaraja ◽  
V. Ganesan ◽  
Omar Bazighifan ◽  
Clemente Cesarano
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Neutral Delay ◽  
Third Order ◽  
Riccati Technique ◽  
Neutral Delay Differential Equations ◽  
The Subject ◽  
Delay Differential ◽  
New Criteria ◽  
Noncanonical Operator

The main purpose of this study is aimed at developing new criteria of the iterative nature to test the asymptotic and oscillation of nonlinear neutral delay differential equations of third order with noncanonical operator (a(ι)[(b(ι)x(ι)+p(ι)x(ι−τ)′)′]β)′+∫cdq(ι,μ)xβ(σ(ι,μ))dμ=0, where ι≥ι0 and w(ι):=x(ι)+p(ι)x(ι−τ). New oscillation results are established by using the generalized Riccati technique under the assumption of ∫ι0ιa−1/β(s)ds<∫ι0ι1b(s)ds=∞asι→∞. Our new results complement the related contributions to the subject. An example is given to prove the significance of new theorem.

Property (A) of third-order advanced differential equations

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
J. Džurina ◽  
B. Baculíková
Keyword(s):  
Differential Equations ◽  
Oscillation Theory ◽  
Comparison Theorems ◽  
Property A ◽  
Third Order ◽  
Nonlinear Functional ◽  
Deviating Argument ◽  
Advanced Argument ◽  
Functional Differential ◽  
Gamma S

AbstractIn the paper we offer criteria for property (A) of the third-order nonlinear functional differential equation with advanced argument $(a(t)(x'(t))^\gamma )'' + p(t)f(x(\sigma (t))) = 0,$, where $\mathop \smallint \limits^\infty a^{ - 1/\gamma } (s)ds = \infty $. We establish new comparison theorems for deducing property (A) of advanced differential equations from that of ordinary differential equations without deviating argument. The presented comparison principle fill the gap in the oscillation theory.

scholarly journals Asymptotic Properties of Solutions to Third-Order Nonlinear Neutral Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Qi Li ◽  
Rui Wang ◽  
Fanwei Meng ◽  
Jianxin Han
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Functional Differential Equations ◽  
Third Order ◽  
Neutral Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Functional Differential

The aim of this work is to discuss asymptotic properties of a class of third-order nonlinear neutral functional differential equations. The results obtained extend and improve some related known results. Two examples are given to illustrate the main results.

scholarly journals Oscillatory behavior of solutions of certain third order mixed neutral differential equations

2013 ◽  
Vol 44 (1) ◽  
pp. 99-112 ◽  
Author(s):  
Ethiraj Thandapani ◽  
Renu Rama
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behavior ◽  
Third Order ◽  
Neutral Differential Equations ◽  
All Solutions ◽  
Positive Integers

The objective of this paper is to study the oscillatory and asymptotic properties of third order mixed neutral differential equation of the form $$ (a(t) [x(t) + b(t) x(t - \tau_{1}) + c(t) x(t + \tau_{2})]'')' + q(t) x^{\alpha}(t - \sigma_{1}) + p(t) x^{\beta}(t + \sigma_{2}) = 0 $$where $a(t), b(t), c(t), q(t)$ and $p(t)$ are positive continuous functions, $\alpha$ and $\beta$ are ratios of odd positive integers, $\tau_{1}, \tau_{2}, \sigma_{1}$ and $\sigma_{2}$ are positive constants. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converge to zero. Some examples are provided to illustrate the main results.

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