Bifurcation and stability of radially symmetric equilibria of a parabolic equation with variable diffusion (Q1121435)

The author studies radially symmetric solutions of a semilinear parabolic equation with concave type nonlinearity and a diffusion coefficient which is a radial function. A detailed bifurcation analysis coupled with maximum principle arguments permits to provide a full description of radially symmetric equilibria (as depending on a bifurcation parameter multiplying the nonlinear term), together with their stability properties. The latter should be meant in a restricted sense, since they are expressed in terms of the sign of the leading eigenvalue of a radially symmetric linearized problem. The paper extends results obtained in the monodimensional case by Hale and Chipot and by Yanagida.