17 research outputs found
Oscillation criteria for second-order nonlinear perturbed differential equations
No full textIn this article, we study the oscillation of solutions to the nonlinear
second-order differential equation
We obtain sufficient conditions for the oscillation of all solutions to
this equation
Second order neutral delay differential equations and their oscillatory criteria derived by linearization
No full textIn this paper, we investigate the oscillatory behavior of second-order neutral delay differential equations with a canonical operator of the form a(x) v (x) �m + C(x, u(φ(x))) = 0. We introduce new monotonicity properties of the non-oscillatory solutions of these equations, which are then used to linearize the equations and derive new oscillatory criteria. The presented results significantly improve upon existing criteria
Üçüncü Basamaktan Bir Diferensiyel Denklem Sınıfının Çözümlerinin Salınımsızlığı Üzerine
No full textSecond order neutral delay differential equations and their oscillatory criteria derived by linearization
No full textIn this paper, we investigate the oscillatory behavior of second-order neutral delay differential equations with a canonical operator of the form
\begin{align*}
\left(a\left({x}\right)\left(v^\prime\left({x}\right)\right)^{m}\right)^\prime+ C\left({x}, u\left(\varphi\left({x}\right)\right)\right) = 0.
\end{align*}
We introduce new monotonicity properties of the non-oscillatory solutions of these equations, which are then used to linearize the equations and derive new oscillatory criteria. The presented results significantly improve upon existing criteria
Oscillation criteria for a certain second-order nonlinear perturbed differential equations
No full textProperties of monotonic solutions to half-linear second-order delay differential equations
No full textThis paper establishes new monotonic properties of nonoscillatory solutions for second-order half-linear functional differential equations with delayed argument (a(r)(u′(r))m)′ = b(r)um(φ(r)) where m ∈ (0, 1). We develop several key monotonicity results for Kneser solutions and use these properties to derive criteria for the elimination of bounded nonoscillatory solutions. Our approach extends known techniques from linear differential equations to the half-linear case, providing new insights into the qualitative behavior of solutions
