Displaying similar documents to “Heteroclinic orbits in plane dynamical systems”

The nonlinearly damped oscillator

Juan Luis Vázquez (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the large-time behaviour of the nonlinear oscillator m x ' ' + f ( x ' ) + k x = 0 , where m , k > 0 and f is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case f ( x ' ) = A | x ' | α - 1 x ' with α real, A > 0 . We characterize the existence and behaviour of fast orbits, i.e., orbits that stop in finite time.

Classification of positive solutions of p -Laplace equation with a growth term

Matteo Franca (2004)

Archivum Mathematicum

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We give a structure result for the positive radial solutions of the following equation: Δ p u + K ( r ) u | u | q - 1 = 0 with some monotonicity assumptions on the positive function K ( r ) . Here r = | x | , x ∈ ℝ n ; we consider the case when n > p > 1 , and q > p * = n ( p - 1 ) n - p . We continue the discussion started by Kawano et al. in [KYY], refining the estimates on the asymptotic behavior of Ground States with slow decay and we state the existence of S.G.S., giving also for them estimates on the asymptotic behavior, both as r → 0 and as r → ∞ . We make use of a Emden-Fowler...