It is shown, under some general conditions on the coefficients of L, that if f(x) is
locally Hölder continuous and
(1.3)
then there exists a bounded solution of (1.2) in Rn when n ≧ 3. If n = 2
then bounded entire solutions may not exist, but there exists a nonnegative
solution of (1.2) in R2 which is bounded above by 0(log|x|). An application
of these results to the Cauchy problem is given in the final section of the
paper.
