# Positive solutions for a semipositone problem involving nonlocal operator

### Ghasem A. Afrouzi

University of Mazandaran, Babolsar, Iran### Nguyen Thanh Chung

Quang Binh University, Vietnam### S. Shakeri

University of Mazandaran, Babolsar, Iran

## Abstract

In this article, we are interested in the existence of positive solutions for the following Kirchhoff type problems

${−M(∫_{Ω}∣∇u∣_{p}dx)div(∣∇u∣_{p−2}∇u)=λa(x)f(u)−μu=0 inΩ,onx∈∂Ω, $

where $Ω$ is a bounded smooth domain of $R_{N},1<p<N,M:R_{0}→R_{+}$ is a continuous and increasing function, $λ,μ$ are two positive parameters, $a∈C(Ω),a(x)≥a_{0}>0$ , and $f$ is a $C_{1}([0,∞))$ function such that $f(0)=0,f(t)>0$ for all $0<t<t_{0}$ and $f(t)≤0$ for all $t≥t_{0}$ , where $t_{0}>0$ .

## Cite this article

Ghasem A. Afrouzi, Nguyen Thanh Chung, S. Shakeri, Positive solutions for a semipositone problem involving nonlocal operator. Rend. Sem. Mat. Univ. Padova 132 (2014), pp. 25–32

DOI 10.4171/RSMUP/132-2