The Existence of Bounded Solutions of a Semilinear Heat Equation

Source abstract

We investigate the existence of bounded solutions of $\Delta w - y\cdot {{\nabla w} / {2 - ({1 / {(p - 1))w + | w |^{p - 1} w}}}} = 0$, $y \in R^N$, for $N > 2$ and $p > {{(N + 2)} / {(N - 2)}}$. We show that if $N = 3$ and $6 \leqq p \leqq 12$ then there are infinitely many positive, bounded, radially symmetric solutions $w(r)$, $r =| y |$, such that$\lim _{r \to \infty } w(r) = 0$.