Properties of unique positive solution for a class of nonlocal semilinear elliptic equation

Ruiting Jiang, Chengbo Zhai


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.


Nonlocal elliptic equation; positive solution; existence and uniqueness; monotone operator; mixed monotone operator

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