Radial ground states and singular ground states for a spatial-dependent p-Laplace equation

AbstractWe consider the following equationΔpu(x)+f(u,|x|)=0, where x∈Rn, n>p>1, and we assume that f is negative for |u| small and limu→+∞f(u,0)u|u|q−2=a0>0 where p∗=p(n−1)n−p<q<p∗=npn−p, so f(u,0) is subcritical and superlinear at infinity.In this paper we generalize the results obtained in a previous paper, [11], where the prototypical nonlinearityf(u,r)=−k1(r)u|u|q1−2+k2(r)u|u|q2−2 is considered, with the further restriction 1<p⩽2 and q1>2. We manage to prove the existence of a radial ground state, for more generic functions f(u,|x|) and also in the case p>2 and 1<q1