Large solutions of semilinear equations with Hardy potential

Abstract

We consider equations of the form $-L_{\mu }u+f(u)=0$ in a smooth domain $\Omega$, where $L_{\mu }=\Delta +\mu {\delta }^{-2}$ and $\delta (x)$ denotes the distance of the point $x$ to the boundary of the domain. The nonlinear term $f$ is positive, increasing and convex on $(0,\infty )$, satisfies the Keller-Osserman condition and some additional technical assumptions. The conditions are satisfied, in particular, by power and exponential nonlinearities. We discuss the question of existence and uniqueness of large solutions when $\mu >0$.

13 pages

References in corpus (1)

• Large solutions to semilinear elliptic equations with Hardy potential and exponential nonlinearity