Our results are not restricted with boundedness of solutions.
📌 3 Key Takeaways
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Objective & Hypothesis:Some oscillation criteria for the following second-order neutral differential equation [x(t)\pm r(t) f( x(t-g))]''+p(t) g(x(t-a)) -q(t) g(x(t-b )) = s(t) where t\geq t0, g,a,b \in R+ with a \geq b, r \in C2([t0,\infty ), R+) , p,q\in C([t0,\infty ),R+) and f,g\in C(R,R), s\in C([ t0,\infty),R) have been obtained.
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Key Findings & Data:Some oscillation criteria for the following second-order neutral differential equation [x(t)\pm r(t) f( x(t-g))]''+p(t) g(x(t-a)) -q(t) g(x(t-b )) = s(t) where t\geq t0, g,a,b \in R+ with a \geq b, r \in C2([t0,\infty ), R+) , p,q\in C([t0,\infty ),R+) and f,g\in C(R,R), s\in C([ t0,\infty),R) have been obtained.
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Conclusion & Impact:Our results are not restricted with boundedness of solutions.
Some oscillation criteria for the following second-order neutral differential equation [x(t)\pm r(t) f( x(t-g))]''+p(t) g(x(t-a)) -q(t) g(x(t-b )) = s(t) where t\geq t0, g,a,b \in R+ with a \geq b, r \in C2([t0,\infty ), R+) , p,q\in C([t0,\infty ),R+) and f,g\in C(R,R), s\in C([ t0,\infty),R) have been obtained. Our results are not restricted with boundedness of solutions.
Özet
Some oscillation criteria for the following second-order neutral differential equation [x(t)\pm r(t) f( x(t-g))]''+p(t) g(x(t-a)) -q(t) g(x(t-b )) = s(t) where t\geq t0, g,a,b \in R+ with a \geq b, r \in C2([t0,\infty ), R+) , p,q\in C([t0,\infty ),R+) and f,g\in C(R,R), s\in C([ t0,\infty),R) have been obtained. Our results are not restricted with boundedness of solutions.
ÖCALAN, Ö., KARPUZ, B., YILDIZ, M. K. (2022). Oscillation of nonlinear neutral delay differential equations of second-order with positive and negative coefficients. Turkish Journal of Mathematics, Cilt: 33 - Sayı: 4, 341–350. https://ajindex.com/articles/608559