A VERY SINGULAR SOLUTION OF A DOUBLY DEGENERATE PARABOLIC EQUATION WITH NONLINEAR CONVECTION

We here investigate an existence and uniqueness of the nontrivial, nonnegative solution of a nonlinear ordinary differential equation: [vertical bar(w(m))'vertical bar(p-2)(w(m))']' + beta rw' + alpha w + (w(q))' = 0 satisfying a specific decay rate: lim(r ->infinity) r(alpha/beta)w(r) = 0 with alpha: = (p - 1)/[pq - (m + 1)(p - 1)] and beta = [q - m(p - 1)]/[pq (m + 1)(p - 1)]. Here m(p - 1) > 1 and m(p - 1) < q < (m + 1)(p - 1). Such a solution arises naturally when we study a very singular solution for a doubly degenerate equation with nonlinear convection: