
Abstract: We are concerned with existence, uniqueness and asymptotic behaviour of positive solutions of a parabolic PDE driven by the p-Laplacian with indefinite and unbounded potentials besides a logistic source having weight which is also indefinite and unbounded. The boundary condition appearing is of flux type, precisely, Neumann or Robin. The asymptotic stability properties of the stationary solutions are described using principal eigenvalues of some elliptic eigenvalue problems.