Periodic solutions of the evolutionary \(p\)-Laplacian with nonlinear sources (Q973989)

The existence of positive periodic solutions of the problem \[ {\partial u\over\partial t}= \text{div}(|\nabla u|^{p-2}\nabla u)+ \alpha(x, t)u^q \] is considered in the domain \(\Omega\times\mathbb{R}\). The lateral condition \(u(x,t)= 0\) is imposed on \(\partial\Omega\times \mathbb{R}\). The function \(\alpha\) is assumed to be periodic: \(\alpha(x,t)= \alpha(x, t+\omega)\). Also some nonexistence results are given in starshaped domains.