Institution: | a Dipartimento di Matematica “U. Dini”, Università degli Studi di Firenze, Viale G.B. Morgagni 67/A, 50134 Firenze, Italy b Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy |
Abstract: | We study the question of asymptotic stability, as time tends to infinity, of solutions of dissipative anisotropic Kirchhoff systems, involving the p(x)-Laplacian operator, governed by time-dependent nonlinear damping forces and strongly nonlinear power-like variable potential energies. This problem had been considered earlier for potential energies which arise from restoring forces, whereas here we allow also the effect of amplifying forces. Global asymptotic stability can then no longer be expected, and should be replaced by local stability. The results are further extended to the more delicate problem involving higher order damping terms. |