The status of and perspectives on the development of the theory of differential equations with deviating argument (IV All-Union Conference on the theory and applications of differential equations)

1976 ◽  
Vol 28 (2) ◽  
pp. 222-225
Author(s):  
Yu. A. Mitropol'skii ◽  
E. Yu. Romanenko ◽  
A. N. Sharkovskii ◽  
V. N. Shevelo
Keyword(s):  
Differential Equations ◽  
Deviating Argument ◽  
The Status ◽  
Union Conference

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.

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