On positive singular solutions for a class of nonhomogeneous \(p\)-Laplacian-like equations (Q1265087)

The paper concerns the asymptotic behaviour, near the isolated singularity at the origin, of positive radial solutions \(u\) to the nonlinear equation \(-\text{div}(A(|\nabla u|)\nabla u)=f(u)\). Let \(N>1\) be the space dimension, let \(\phi(s)=sA(s)\), and let \(C\) be a positive parameter. Existence and behaviour of positive solutions \(u\) on \((0,R)\) to the differential systems \(-(r^{N-1}\phi(u'))'=r^{N-1}f(u)\), \(u(R)=0\), \(-R^{N-1}\phi(u'(R))=C\) are investigated through the behaviour of positive solutions \(h\) on \((0,R)\) to the differential systems \(-(r^{N-1}\phi(h'))'=0\), \(h(R)=0\), \(-R^{N-1}\phi(h'(R))=C\). A typical hypothesis states \(\lim_{r\to 0^+}h(r)=+\infty\), whereas typical results look like \(\lim_{r\to 0^+}u(r)=+\infty\).