Existence of multiple equilibrium points in global attractor for damped wave equation

Autor:	Fengjuan Meng, Cuncai Liu, Chang Zhang
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Lyapunov functional Global attractor Z 2 $Z_{2}$ index Equilibrium points Wave equation Analysis QA299.6-433
Zdroj:	Boundary Value Problems, Vol 2019, Iss 1, Pp 1-9 (2019)
Druh dokumentu:	article
ISSN:	1687-2770
DOI:	10.1186/s13661-019-1123-2
Popis:	Abstract This paper is a continuation of Meng and Zhong in (Discrete Contin. Dyn. Syst., Ser. B 19:217–230, 2014). We go on studying the property of the global attractor for some damped wave equation with critical exponent. The difference between this paper and Meng and Zhong in (Discrete Contin. Dyn. Syst., Ser. B 19:217–230, 2014) is that the origin is not a local minimum point but rather a saddle point of the Lyapunov function F for the symmetric dynamical systems. Using the abstract result established in Zhang et al. in (Nonlinear Anal., Real World Appl. 36:44–55, 2017), we prove the existence of multiple equilibrium points in the global attractor for some wave equations under some suitable assumptions in the case that the origin is an unstable equilibrium point.
Databáze:	Directory of Open Access Journals
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