Global existence and asymptotic behavior of solutions for a system of higher-order Kirchhoff-type equations

Existence and Asymptotic Behavior of Global Solutions for a Class of Nonlinear Higher-Order Wave Equation

The initial boundary value problem for a class of nonlinear higher-order wave equation with damping and source term utt Au a|ut|ut b|u|q−1u in a bounded domain is studied, where A −Δ , m ≥ 1 is a nature number, and a, b > 0 and p, q > 1 are real numbers. The existence of global solutions for this problem is proved by constructing the stable sets and shows the asymptotic stability of the global ...

Existence and Asymptotic Behavior of Solutions for Hénon Type Equations

This paper is concerned with ground state solutions for the Hénon type equation −∆u(x) = |y|αup−1(x) in Ω, where Ω = B(0, 1) × Bn−k(0, 1) ⊂ R and x = (y, z) ∈ R × Rn−k. We study the existence of cylindrically symmetric and non-cylindrically symmetric ground state solutions for the problem. We also investigate asymptotic behavior of the ground state solution when p tends to the critical exponent...

Blow up of Solutions for a System of Nonlinear Higher-order Kirchhoff-type Equations

In this work, we consider the initial boundary value problem for the Kirchhoff-type equations with damping and source terms  utt +M (∫ Ω ∣∣∣(−△)m2 u∣∣∣2 dx) (−△) u+ |ut| ut = f1 (u, v) , vtt +M (∫ Ω ∣∣∣(−△)m2 v∣∣∣2 dx) (−△) v + |vt| vt = f2 (u, v) in a bounded domain. We prove the blow up of the solution with positive initial energy by using the technique of [26] with a modification in th...

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...

Global Existence and Asymptotic Behavior of Solutions for a Class of Nonlinear Degenerate Wave Equations