Threshold Result for Semilinear Parabolic Equations with Indefinite Non-Homogeneous Term

In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations equation(P){ut-Δu=g(u)+λf(x),(x,t)∈Ω×(0,T),u=0,(x,t)∈∂Ω×(0,T),u(x,0)=u0(x)≥0,x∈Ω. By combining a priori estimate of global solution with property of stationary solution set of problem (P), we prove that the minimal stationary solution Uλ(x) of problem (P) is stable, whereas, any other stationary solution is an initial datum threshold for the existence and nonexistence of global solution to problem (P).