Bifurcation from interval and positive solutions of Minkowski-curvature on unbounded domain

Abstract

We construct the bifurcation of interval of positive radial solutions from the trivial solution to the following Minkowski-curvature problems on unbounded domains$-\text{div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u{|}^2}}\right)=\lambda f(x,u),x\in R^N,$$u\to 0,\text{as}\left|x\right|\to +\infty ,$ where f is not necessarily linearizable at zero. The proof of main results are based on the topological degree and global bifurcation techniques.