scholarly journals Property (A) and Oscillation of Third-Order Differential Equations with Mixed Arguments

2012 ◽  
Vol 55 (2) ◽  
pp. 239-253 ◽  
Author(s):  
B. Baculíková ◽  
J. Džurina
Keyword(s):  
Differential Equations ◽  
Property A ◽  
Third Order ◽  
Mixed Arguments

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.

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 Some Properties of Third-Order Differential Equations with Mixed Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
B. Baculíková ◽  
J. Džurina
Keyword(s):  
Differential Equations ◽  
General Equation ◽  
Third Order ◽  
Deviating Arguments ◽  
Mixed Arguments

We offer a new comparison the principle for deducing properties of third-order differential equations with mixed arguments,(r(t)[x'(t)]γ)′′+q(t)f(x(τ(t)))+p(t)h(x(σ(t)))=0, from those of the corresponding differential equations, without deviating arguments. The presented technique permits to extend immediately the results known for an equation without deviating arguments to a more general equation with advanced and delay arguments.

scholarly journals On Third Order Differential Equations with Property A and B

1999 ◽  
Vol 231 (2) ◽  
pp. 509-525 ◽  
Author(s):  
Mariella Cecchi ◽  
Zuzana Došlá ◽  
Mauro Marini
Keyword(s):  
Differential Equations ◽  
Property A ◽  
Third Order

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

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