The global asymptotic stability of the rest point for nonlinear equations has been studied by Levin & Nohel, by Artstein & Infante, We extended this studies to extremals of scalar variational problems in Section 5 of our paper [P. Pucci and J. Serrin, Continuation and limit properties for solutions of strongly nonlinear second order differential equations, Asymptotic Anal. 4 (1991), 97–160], where the Euler-Lagrange equation exhibits even stronger nonlinearities. In this paper we treat the nontrivial case when the extremals are vectorial. We show that the results of our previous papers carry over to the vector case in a surprisingly close way, enough even to suggest that it is the variational character of the nonlinear system, more than anything else, which produces the desired asymptotic stability.
Global asymptotic stability for strongly nonlinear second order systems
PUCCI, Patrizia;
1992
Abstract
The global asymptotic stability of the rest point for nonlinear equations has been studied by Levin & Nohel, by Artstein & Infante, We extended this studies to extremals of scalar variational problems in Section 5 of our paper [P. Pucci and J. Serrin, Continuation and limit properties for solutions of strongly nonlinear second order differential equations, Asymptotic Anal. 4 (1991), 97–160], where the Euler-Lagrange equation exhibits even stronger nonlinearities. In this paper we treat the nontrivial case when the extremals are vectorial. We show that the results of our previous papers carry over to the vector case in a surprisingly close way, enough even to suggest that it is the variational character of the nonlinear system, more than anything else, which produces the desired asymptotic stability.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
