All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 15 Next

Displaying 281 – 300 of 1511

Showing per page

Attractors of Strongly Dissipative Systems

A. G. Ramm (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947...

Bifurcation of free vibrations for completely resonant wave equations

Massimiliano Berti, Philippe Bolle (2004)

Bollettino dell'Unione Matematica Italiana

We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency ω belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.

Bifurcation theorems for nonlinear problems with lack of compactness

Francesca Faraci, Roberto Livrea (2003)

Annales Polonici Mathematici

We deal with a bifurcation result for the Dirichlet problem ⎧ - Δ p u = μ / | x | p | u | p - 2 u + λ f ( x , u ) a.e. in Ω, ⎨ ⎩ u | ∂ Ω = 0 . Starting from a weak lower semicontinuity result by E. Montefusco, which allows us to apply a general variational principle by B. Ricceri, we prove that, for μ close to zero, there exists a positive number λ * μ such that for every λ ∈ ] 0 , λ * μ [ the above problem admits a nonzero weak solution u λ in W ₀ 1 , p ( Ω ) satisfying l i m λ → 0 ⁺ | | u λ | | = 0 .

Currently displaying 281 – 300 of 1511