## Topological Methods in Nonlinear Analysis

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

#### Abstract

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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 50, Number 2 (2017), 669-682.

Dates
First available in Project Euclid: 11 October 2017

https://projecteuclid.org/euclid.tmna/1507687549

Digital Object Identifier
doi:10.12775/TMNA.2017.036

Mathematical Reviews number (MathSciNet)
MR3747033

Zentralblatt MATH identifier
06836838

#### Citation

Jiang, Ruiting; Zhai, Chengbo. Properties of unique positive solution for a class of nonlocal semilinear elliptic equation. Topol. Methods Nonlinear Anal. 50 (2017), no. 2, 669--682. doi:10.12775/TMNA.2017.036. https://projecteuclid.org/euclid.tmna/1507687549

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