Large solutions of degenerate and/or singular quasilinear elliptic equations in a ball

Abstract

We consider local weak large solutions with its blow-up rate near the boundary to certain class of degenerate and/or singular quasilinear elliptic equation\\ $\mathrm{div}(d^{\alpha }(x,\partial B){\Phi }_p(\nabla u))=b(x)f(u)$ in a ball B, where $f$ is normalized regularly varying at infinity with index $\sigma +1>p-1,p>1$. In particular, how the asymptotic behavior of the solution changes over the varying index and degeneracy and/ or singularity present in the equation. We also include the second order blow-up rate for the corresponding semilinear problem.