TY - JOUR AU - Jiang, Ruiting AU - Zhai, Chengbo PY - 2017/10/09 Y2 - 2024/03/28 TI - Properties of unique positive solution for a class of nonlocal semilinear elliptic equation JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 50 IS - 2 SE - DO - UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2017.036 SP - 669 - 682 AB - We study a class of nonlocal elliptic equations $$ -M\bigg(\int_{\Omega}|u|^{\gamma}dx\bigg)\Delta u=\lambda f(x,u) $$ with the Dirichlet boundary conditions in bounded domain. Under suitable assumptions on $M$ and the nonlinear term $f$, the existence and new properties of a unique positive solutions are obtained via a monotone operator method and a mixed monotone operator method. ER -