Existence results of positive solutions for Kirchhoff type equations via bifurcation methods

2017/10/05 by Cintra, Willian, Júnior, João R. Santos, Siciliano, Gaetano +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.02120

Abstract

In this paper we address the following Kirchhoff type problem \ -Δ(g(|∇ u|₂²) u + u^r) = a u + b u^p · amp; in~Ω, u · gt;0 · amp; in~Ω, u= 0 · amp; on~∂Ω, . in a bounded and smooth domain Ω in \rm I\hskip -0.85mm\rm R. By using change of variables and bifurcation methods, we show, under suitable conditions on the parameters a,b,p,r and the nonlinearity g, the existence of positive solutions.

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