Calculus of Variations and Geometric Measure Theory

Q. H. Nguyen - L. VĂ©ron

Wiener criteria for existence of large solutions of quasilinear elliptic equations with absorption

created by nguyen on 22 Jul 2018


Published Paper

Inserted: 22 jul 2018
Last Updated: 22 jul 2018

Journal: Potential Analysis
Pages: 17
Year: 2015


We obtain sufficient conditions, expressed in terms of Wiener type tests involving Hausdorff or Bessel capacities, for the existence of large solutions to equations (1) $-\Delta_pu+e^{ u}-1=0$ or (2) $-\Delta_pu+ u^q=0$ in a bounded domain $\Omega$ when $q>p-1>0$. We apply our results to equations (3) $-\Delta_pu+a\
\nabla u\
^{q}+bu^{s}=0$, (4) $\Delta_p u+u^{-\gamma}=0$ with $1<p\le 2$, $1\le q\le p$, $a>0, b>0$ and $q>p-1$, $s\geq p-1$, $\gamma>0$.