Bifurcation of positive solutions of elliptic Kirchhoff equations involving gradient terms
Abstract
We prove several existence and multiplicity results for some nonlinear elliptic Kirchhoff equations {−(1+γG′(∫Ω|∇u|2dx))Δu=f(x,u,∇u),x∈Ω,u(x)=0,x∈∂Ω, where γ>0 is a parameter, G:R+→R and f:Ω×R+×RN→R are smooth functions satisfying C1tq−1≤G′(t)≤C2tq−1∀t∈[0,∞),C3|u|p−1≤f(x,u,v)≤C4|u|p−1∀(x,u,v)∈Ω×R+×RN, Ci(i=1,2,3,4) are constants and q>1, 2
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Complex Variables and Elliptic Equations
- Pages
- 1–14
- Publication date
- 14 January 2026
- Language
- EN