Decaying entire positive solutions of quasilinear elliptic equations

The quasilinear elliptic equation (^*)u+f(x,u,u)=0 is considered in the whole Euclidean space ^N,N3. Under suitable structure hypotheses it is shown that (^*) has an entire positive solution which decays to zero at infinity. In particular, conditions are established for the existence of an entire positive solution of (^*) which behaves like a constant multiple of |x|^2–N as |x|.Supported in part by Grant-in-Aid for Scientific Research (No. 5860004), Ministry of Education (Japan).Research supported by NSERC (Canada) under Grant A-3105.