On Similarity Solutions of a Heat Equation with a Nonhomogeneous Nonlinearity

We are interested in positive radially symmetric solutions of the semilinear equation where p>1, l>−2 and A≡ . This equation is satisfied by self-similar solutions of a semilinear heat equation. We prove existence and non existence of solutions for various values of the parameters l and p. When solutions exist we study their asymptotic behavior and discuss their uniqueness. Our proofs are based on various continuity, comparison and Pohozaev type arguments.