Soluções clássicas para uma equação elíptica semilinear não homogênea

Abstract

This work is mainly concerned with the existence and nonexistence of classical solution to the nonhomogeneous semilinear equation Δu + up + f(x) = 0 in Rn, u > 0 in Rn, when n 3, where f 0 is a Hölder continuous function. The nonexistence of classical solution is established when 1 < p n=(n 􀀀 2). For p > n=(n 􀀀 2) there may be both existence and nonexistence results depending on the asymptotic behavior of f at infinity. The existence results were obtained by employed sub and supersolutions techniques and fixed point theorem. For the nonexistence of classical solution we used a priori integral estimates obtained via averaging.