Oscillation and Asymptotic Properties of Differential Equations of Third-Order

Oscillation of Third-order Functional Differential Equations

The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear delay differential equation (E) ˆ a(t) ˆ x ′′(t) ̃ γ ̃ ′ + q(t)f(x [τ (t)]) = 0. Applying suitable comparison theorems we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of (E). Obtained results essentially improve and complement earlier ones. Variou...

Asymptotic Properties of Third-Order Delay Trinomial Differential Equations

and Applied Analysis 3 2. Main Results It will be derived that properties of E are closely connected with the corresponding secondorder differential equation ( 1 r t v′ t )′ p t v t 0 Ev as the following theorem says. Theorem 2.1. Let v t be a positive solution of Ev . Then E can be written as ( v2 t r t ( 1 v t y′ t )′)′ q t v t y σ t 0. E Proof. The proof follows from the fact that 1 v t ( v2...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Oscillation and Asymptotic Behavior of Higher-Order Nonlinear Differential Equations

Oscillation of third order trinomial delay differential equations

The purpose of this paper is to study oscillation and asymptotic behavior of solutions to a third order linear delay differential equation . All righ in part t Umeå Baculíko y000ðtÞ þ pðtÞy0ðtÞ þ qðtÞyðsðtÞÞ 1⁄4 0: New comparison theorems deduce oscillation of the given third order delay differential equation via application of known oscillation criteria to associated first order delay differen...