The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first. Then the result of nonexistence for differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blow-up estimate for a class quasilinear reaction-diffusion systems (non-Newtonian filtration systems) are established to extend the result of semilinear reactiondiffusion (Fujita type) systems.

This paper deals with grazing rub-impact dynamics in a rotor system by using the rub-impact Poincar

Integer multiple spiking induced by Gaussian white noise in the stochastic Chay system may occur near a subcritical Hopf bifurcation of the corresponding deterministic system without external periodic forcing. The deterministic Chay system near the subcritical Hopf bifurcation can exhibit a damped subthreshold oscillation of membrane potential, and can easily fire a spike in response to some kinds of weak pulses. Therefore, on account of the characteristic of Gaussian white noise, it can be shown that the deterministic Chay system supplied with certain weak pulses can fire integer multiple spiking similar to that in the corresponding stochastic system. Furthermore, on the light of the characteristic of the unstable limit cycle "before" a subcritical Hopf bifurcation in the deterministic Chay model, it can be explained that integer multiple spiking only appears in a certain range of the parameter VK.

In this paper, some suffcient conditions under which the quasilinear elliptic system −div(|∇u|p−2∇u)=um1vn1;−div(|∇u|q−2∇u) =um2vn2 in RN (N¿3) has no radially symmetric positive solution is derived. Then by using this non-existence result, blow-up estimates for a class of quasilinear reaction-diffusion systems ut=div(|∇u|p−2∇u)+um1vn1; vt=div(|∇v|q−2∇v)+um2vn2 with the homogeneous Dirichlet boundary value conditions are obtained. Copyright ? 2003 John Wiley & Sons, Ltd.

The prior estimate and decaypropertyof positive solutions are derived for a system of quasilinear elliptic diserential equations 3rst. Then, the nonexistence result for radiallynonincreasing positive solutions of the sys11 tem is implied. Byusing this nonexistence result, blow-up estimates for a class of quasilinear reaction-diffusion systems (non-Newtonian 3ltration systems) are established to extend the result for semilinear reaction-disusion 13 systems (Fujita type).