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Displaying 441 –
460 of
9351
We consider the problem of the existence of positive solutions u to the problem
,
(g ≥ 0,x > 0, n ≥ 2).
It is known that if g is nondecreasing then the Osgood condition
is necessary and sufficient for the existence of nontrivial solutions to the above problem. We give a similar condition for other classes of functions g.
Saddle connections and subharmonics are investigated for a class of forced second order differential equations which have a fixed saddle point. In these equations, which have linear damping and a nonlinear restoring term, the amplitude of the forcing term depends on displacement in the system. Saddle connections are significant in nonlinear systems since their appearance signals a homoclinic bifurcation. The approach uses a singular perturbation method which has a fairly broad application to saddle...
We extend the classical Leighton comparison theorem to a class of quasilinear forced second order differential equations
where the endpoints , of the interval are allowed to be singular. Some applications of this statement in the oscillation theory of (*) are suggested.
We consider differential inclusions where
a positive semidefinite function of the solutions satisfies a
class- estimate
in terms of time and a second positive semidefinite function of the
initial condition.
We show that a smooth converse Lyapunov function, i.e., one whose
derivative along solutions can be
used to establish the class- estimate, exists if and
only if the class- estimate
is robust, i.e., it holds for a larger, perturbed differential
inclusion.
It remains an open question whether...
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9351