Existence of positive solutions for Kirchhoff type equations

• Main Authors: Ghasem A. Afrouzi, Nguyen Thanh Chung, Saleh Shakeri
• Format: Article
• Language: English
• Published: Texas State University 2013-08-01
• Series: Electronic Journal of Differential Equations
• Subjects: Kirchhoff type problems; semipositone; positive solution; sub-supersolution method
• Online Access: http://ejde.math.txstate.edu/Volumes/2013/180/abstr.html
• ISSN: 1072-6691

In this article, we are interested in the existence of positive solutions for the Kirchhoff type problems $$displaylines{ -MBig(int_{Omega}|abla u|^p,dxBig)Delta_pu = lambda f(u) quad hbox{in } Omega,cr u > 0 quad hbox{in } Omega, quad u =0 quad hbox{on } partialOmega, }$$ where $ 1<p< N $, $M : mathbb{R}^+o mathbb{R}^+$ is a continuous and increa sing function, $ lambda $ is a parameter, $ f: [0,+infty) o mathbb{R} $ is a $ C^1 $ nondecreasing function satisfying $ f(0)<0 $ (semipositone). Our proof is based on the sub- and super-solutions techniques.