A criterion is established on the bounded solutions of type higher-order nonlinear neutral differential equations of type oscillatory or tending to zero at infinity [a(t) [x(t)+r(t)x(k(t))]^{(n-1]' +p(t)F(x(t(t)))+q(t)G(x(s(t)))= f(t), where t\geq t0, n\geq 2, a,p are positive, r,q,f are allowed to alternate in sign infinitely many times, F,G are continuous functions, and k,t,s are strictly increasing unbounded continuous delay functions.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:A criterion is established on the bounded solutions of type higher-order nonlinear neutral differential equations of type oscillatory or tending to zero at infinity [a(t) [x(t)+r(t)x(k(t))]^{(n-1]' +p(t)F(x(t(t)))+q(t)G(x(s(t)))= f(t), where t\geq t0, n\geq 2, a,p are positive, r,q,f are allowed to alternate in sign infinitely many times, F,G are continuous functions, and k,t,s are strictly increasing unbounded continuous delay functions.
📊
Key Findings & Data:A criterion is established on the bounded solutions of type higher-order nonlinear neutral differential equations of type oscillatory or tending to zero at infinity [a(t) [x(t)+r(t)x(k(t))]^{(n-1]' +p(t)F(x(t(t)))+q(t)G(x(s(t)))= f(t), where t\geq t0, n\geq 2, a,p are positive, r,q,f are allowed to alternate in sign infinitely many times, F,G are continuous functions, and k,t,s are strictly increasing unbounded continuous delay functions.
💡
Conclusion & Impact:A criterion is established on the bounded solutions of type higher-order nonlinear neutral differential equations of type oscillatory or tending to zero at infinity [a(t) [x(t)+r(t)x(k(t))]^{(n-1]' +p(t)F(x(t(t)))+q(t)G(x(s(t)))= f(t), where t\geq t0, n\geq 2, a,p are positive, r,q,f are allowed to alternate in sign infinitely many times, F,G are continuous functions, and k,t,s are strictly increasing unbounded continuous delay functions.
A criterion is established on the bounded solutions of type higher-order nonlinear neutral differential equations of type oscillatory or tending to zero at infinity [a(t) [x(t)+r(t)x(k(t))]^{(n-1]' +p(t)F(x(t(t)))+q(t)G(x(s(t)))= f(t), where t\geq t0, n\geq 2, a,p are positive, r,q,f are allowed to alternate in sign infinitely many times, F,G are continuous functions, and k,t,s are strictly increasing unbounded continuous delay functions.
Özet
A criterion is established on the bounded solutions of type higher-order nonlinear neutral differential equations of type oscillatory or tending to zero at infinity [a(t) [x(t)+r(t)x(k(t))]^{(n-1]' +p(t)F(x(t(t)))+q(t)G(x(s(t)))= f(t), where t\geq t0, n\geq 2, a,p are positive, r,q,f are allowed to alternate in sign infinitely many times, F,G are continuous functions, and k,t,s are strictly increasing unbounded continuous delay functions.