
Journal of Convex Analysis 26 (2019), No. 4, 11751186 Copyright Heldermann Verlag 2019 Asymptotic Behavior of Solutions to a SecondOrder Gradient Equation of PseudoConvex Type Hadi Khatibzadeh Department of Mathematics, University of Zanjan, P. O. Box 45195313, Zanjan, Iran hkhatibzadeh@znu.ac.ir Gheorghe Morosanu Faculty of Mathematics and Computer Science, BabesBolyai University, 1 M. Kogalniceanu Street, 400084 ClujNapoca, Romania morosanu@math.ubbcluj.ro [Abstractpdf] 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, pseudoconvex 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, pseudoconvex function, minimum point, critical point, second order gradient system, asymptotic behavior. MSC: 34D05, 34D23, 34D20, 34G20 [ Fulltextpdf (107 KB)] for subscribers only. 