Properties of unique positive solution for a class of nonlocal semilinear elliptic equation
Słowa kluczowe
Nonlocal elliptic equation, positive solution, existence and uniqueness, monotone operator, mixed monotone operatorAbstrakt
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.Bibliografia
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