The eigenvalue problem for the p-Laplace operator with Robin boundary conditions is considered in this paper. A Faber-Krahn type inequality is proved. More precisely, it is shown that amongst all the domains of fixed volume, the ball has the smallest first eigenvalue.
In this paper, we will analyze further to obtain a finer asymptotic behavior of positive solutions of semilinear elliptic equations in R^n by employing the Li＇s method of energy function.
In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g（μ）＋λf（x）,（x,t）∈Ω×（0,T）,μ=0,（x,t）∈ Ω×[0,T）,μ（x,0）=μ0（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）.
