Considering the stationary pattern of a kind of food chain model with prey-dependent functional response,we get the upper and lower bounds of the stationary pattern s positive solution and the condition without the nonconstant solution.

By use of upper and lower solution method and maximum and minimum principle,the estimates of blow-up rates for the positive solution of the heat equation with a nonlinear reaction term and a nonlinear boundary condition are presented,and the upper and lower bounds of the estimates have been got.

In this paper, based on the relationship between the minimal eigenvalue and the spectral radius of nonuegative matrices, we derive some others upper and lower bounds on irreducible, M-matrices.