Global existence and asymptotic behavior of solutions for thermodiffusion equations

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...

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

Existence and Asymptotic Behavior of Solutions for Hénon Equations in Hyperbolic Spaces

In this article, we consider the existence and asymptotic behavior of solutions for the Hénon equation −∆BN u = (d(x)) α|u|p−2u, x ∈ Ω u = 0 x ∈ ∂Ω, where ∆BN denotes the Laplace Beltrami operator on the disc model of the Hyperbolic space BN , d(x) = dBN (0, x), Ω ⊂ BN is geodesic ball with radius 1, α > 0, N ≥ 3. We study the existence of hyperbolic symmetric solutions when 2 < p < 2N+2α N−2 ....

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 ...

Global asymptotic behavior for delay dynamic equations

We give conditions under which the trivial solution of a first-order nonlinear variable-delay dynamic equation is asymptotically stable, for arbitrary time scales that are unbounded above. In an example, we apply our techniques to a logistic dynamic equation on isolated, unbounded time scales. c © 2006 Elsevier Ltd. All rights reserved. MSC: 39A10; 34B10