Estudo de uma classe de equações elípticas semilineares em Rn - Santos, Tatiane Carvalho (2011)
In this work we study the semilinear elliptic equation -u + jujp + f (x) = 0 in Rn, where n - 3, p > n-(n - - 2) and f is a Hölder continuous function. Assuming a growth condition on f at in nity we discuss the existence of classical solution. Furthermore, we prove a comparison principle and as a consequence we obtain results of non-existence and uniqueness of classical solution in a certain class of functions. To get the result of existence, we use the Schauder Fixed Point Theorem. The non-existence and uniqueness of solution is obtained by using the method of sub and supersolution with a priori integral estimates.