Pairs of positive solutions of quasilinear elliptic equations in exterior domains (Q1070427)

Under suitable assumptions on f and q it is proved that the boundary value problem \[ (1)\quad \Delta u-q(| x|)u=f(x,u,\nabla u) \] in \(\Omega a=\{x\in R^ n:\) \(| x| >\alpha \}\), \(u=0\) in \(\partial \Omega_ a\) has infinitely many solutions. To this end the authors use the method of sub- and supersolutions which are found as spherically symmetric solutions of equation (1) where f is replaced by radial majorants.