217 research outputs found
Upper Bounds for the Blow Up Time for the Kirchhoff-Type Equation
No full textPiskin, Erhan/0000-0001-6587-4479; Dinc, Yavuz/0000-0003-0897-4101; Tunc, Cemil/0000-0003-2909-8753. In this research, we take into account the Kirchhoff type equation with variable exponent. The Kirchhoff type equation is known as a kind of evolution equations,namely, PDEs, where t is an independent variable. This type problem can be extensively used in many mathematical models of various applied sciences such as flows of electrorheological fluids, thin liquid films, and so on. This research, we investigate the upper bound for blow up time under suitable conditions
Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments
No full textIn this article, the author studies the stability and boundedness of solutions for the non-autonomous third order differential equation with a deviating argument, :
\begin{equation*}
\begin{array}{c}
x^{\prime \prime \prime }(t)+a(t)x^{\prime \prime }(t)+b(t)g_{1}(x^{\prime}(t-r))+g_{2}(x^{\prime}(t))+h(x(t-r)) \\
=p(t,x(t),x(t-r),x^{\prime }(t),x^{\prime }(t-r),x^{\prime \prime }(t)),
\end{array}
\end{equation*}
where is a constant. Sufficient conditions are obtained; a stability result in the literature is improved and extended to the preceding equation for the case and a new boundedness result is also established for the case $p(t,x(t),x(t-r),x^{\prime }(t),x^{\prime}(t-r),x^{\prime \prime }(t))\neq 0.
New stability and boundedness results of Liénard type equations with multiple deviating arguments
No full textThe paper considers a Li,nard type equation withmultiple variable deviating arguments. Some sufficient conditions, under which the solution of this equation is asymptotically stable and bounded by means of the Lyapunov functional approach, are found. An example showing the effectiveness of the result is given
Sobre la inestabilidad de ecuaciones diferenciales funcionales no lineales de orden cinco
No full textThe author gives sufficient conditions for non-existence of periodic solutions of two higher order nonlinear delay differential systems. Our technical approach is based on the construction of two suitable Lyapunov type functionals. An example is given to illustrate the obtained results. The main results here improve recent results found on the topic in the literature from the case of without delay to the delay case.El autor presenta condiciones suficientes para la existencia de soluciones periódicas de dos ecuaciones diferenciales con retraso de alto orden. El enfoque técnico se fundamenta en la construcción de funcionales de Lyapunov adecuados. Un ejemplo ilustra los resultados obtenidos. El resultado principal presentado en este artículo mejora un resultado reciente en el tema de pasar el caso sin atraso al caso con atraso
Asymptotic Stability of a Certain Third-order Delay Differential Eqution
No full text通过定义一个Lyapunov泛函,研究如下三阶非线性时滞微分方程解的渐近稳定性:xm(t)+g1(x(t),x’(t))x″(t)+g2(x(t),x’(t))x’(t)+f(x(t-r(t)),x’(t-r(t)))+h(x(t-r(t)))=0.得到的稳定性结果推广了Cemil Tunc[1]的研究结果.By defining a Lyapunov functional, we investigate the asymptotic stability of zero solution to the following third-order nonlinear delay differential equation： x″′（t）＋g1（x（t）,x＇（t））″（t）＋g2（x（t）,x＇（t））x＇（t）＋f（x（t-r（t））,x＇（t-r（t）））＋h（x（t-r（t）））=0. The stability theorem obtained in this paper promotes the result of Cemil Tunc[1]
Instability for a Certain Functional Differential Equation of Sixth Order
No full textSucient conditions are obtained for the instability of the zero solutionof a certain sixth order nonlinear functional dierential equation by the Lyapunov-Krasovskii functional approach. DOI : http://dx.doi.org/10.22342/jims.17.2.7.123-12
On the instability of nonlinear functional differential equations of fifth order
No full textThe author gives sufficient conditions for non-existence of periodic solutions of two higher order nonlinear delay differential systems. Our technical approach is based on the construction of two suitable Lyapunov type functionals. An example is given to illustrate the obtained results. The main results here improve recent results found on the topic in the literature from the case of without delay to the delay case.El autor presenta condiciones suficientes para la existencia de soluciones periódicas de dos ecuaciones diferenciales con retraso de alto orden. El enfoque técnico se fundamenta en la construcción de funcionales de Lyapunov adecuados. Un ejemplo ilustra los resultados obtenidos. El resultado principal presentado en este artículo mejora un resultado reciente en el tema de pasar el caso sin atraso al caso con atraso
On some qualitative behaviors of solutions to a kind of third order nonlinear delay differential equations
No full textSufficiency criteria are established to ensure the asymptotic stability and boundedness of solutions to third-order nonlinear delay differential equations of the form
\begin{equation*}
\begin{array}{c}
\dddot{x}(t)+e(x(t),\dot{x}(t),\ddot{x}(t))\ddot{x}(t)+g(x(t-r),\dot{x}
(t-r))+\psi (x(t-r)) \\
=p(t,x(t),x(t-r),x^{\prime }(t),x^{\prime }(t-r),x^{\prime \prime }(t)).
\end{array}
\end{equation*}
By using Lyapunov's functional approach, we obtain two new results on the subject, which include and improve some related results in the relevant literature. Two examples are also given to illustrate the importance of results obtained
New Ultimate Boundedness and Periodicity Results for Certain Third-order Nonlinear Vector Differential Equations
No full textThe principle aim of this paper is to present some new
results related to the ultimate boundedness and existence of periodic of solutions a certain non-linear ordinary vector differential equation of third order. Our results improve some well-known results in the literature.</p
A Note on Certain Qualitative Properties of a Second Order Linear Differential System
No full textIn this note, two theorems are presented concerning the well known second order linear differential system ¨X +a(t)X =P(t). While the results are not new, the proofs presented simplify previous works since the Gronwall inequality is avoided which is the usual case. The technique of proof involves the integral test and examples are included to illustrate the results
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