Pii: S0893-9659(00)00027-6
نویسنده
چکیده
g e y w o r d s N o n a n t o n o m o u s equation, Wave equation, Uniform attractor, Exponential attractor, a-contraction, Squeezing property. 1 . I N T R O D U C T I O N In this note, we s tudy the long t ime behavior of a general wave equat ion of the form Pu" + Qu' + Au + F (t, u) = h (t) , (1.1) in a Hilbert space H, where A, P , and Q are linear positive self-adjoint operators. This class of equat ions contains different types of wave equat ions previously studied (see [1-5] and the references therein). For instance, this class of equations contains the Sine-Gordon equat ion (see [5]) u" + au' Au + j3 sin u ---f ( t ) , c~ > 0, (1.2) which models the dynamics of a Josephson junct ion driven by a current source. The forcing t e rm f is propor t ional to the current intensi ty applied to the junct ion, it is thus, na tura l to 0893-9659/00/$ see front matter (~) 2000 Elsevier Science Ltd. All rights reserved. Typeset by ~AA,~S-TEX PII: S0893-9659(00)00027-6
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An oscillation criterion for a class of nonlinear functional differential equations
We present a new oscillation criterion for a class of second-order nonlinear functional differential equations obtained by using the integral averaging technique. @ 2000 Elsevier Science Ltd. All rights reserved.
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تاریخ انتشار 2001