Nonexistence of Radial Positive Solutions for A Quasilinear Elliptic Equations Nonpositone Problems in an Annulus

In this paper, our main purpose is studying the nonexistence of radial positive solutions for the boundary-value problem: { −4p u = λf(u(x)), x ∈ Ω; u(x) = 0, x ∈ ∂Ω. where p > 1,λ > 0, Ω is an annulus in R (N > 2) i.e. Ω={x ∈ R |R < |x| < R}(0 < R < R), f is a continuous nonlinear function and satisfies f(0) < 0 (the nonpositone case), f also has more than one zero.