Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article
 


Journal of Convex Analysis 26 (2019), No. 4, 1175--1186
Copyright Heldermann Verlag 2019



Asymptotic Behavior of Solutions to a Second-Order Gradient Equation of Pseudo-Convex Type

Hadi Khatibzadeh
Department of Mathematics, University of Zanjan, P. O. Box 45195-313, Zanjan, Iran
hkhatibzadeh@znu.ac.ir

Gheorghe Morosanu
Faculty of Mathematics and Computer Science, Babes-Bolyai University, 1 M. Kogalniceanu Street, 400084 Cluj-Napoca, Romania
morosanu@math.ubbcluj.ro



[Abstract-pdf]

Consider in a real Hilbert space $H$ the second order gradient equation $$ u''(t) = \nabla \phi(u(t)), \ \ \ t\geq0 . $$ We state and prove several results on the weak or strong convergence of bounded solutions of this equation to minimizers of $\phi$, where $\phi\colon H\to \mathbb{R}$ is a continuously differentiable, pseudo-convex function with ${\rm Argmin}\,\phi\neq\varnothing$. Our results extend previous results in the literature that are related to the case when $\phi$ is convex.

Keywords: Convex function, pseudo-convex function, minimum point, critical point, second order gradient system, asymptotic behavior.

MSC: 34D05, 34D23, 34D20, 34G20

[ Fulltext-pdf  (107  KB)] for subscribers only.