Continuum of one‐sign solutions of one‐dimensional Minkowski‐curvature problem with nonlinear boundary conditions

In this work, we investigate the continuum of one‐sign solutions of the nonlinear one‐dimensional Minkowski‐curvature equation with nonlinear boundary conditions by using unilateral global bifurcation techniques. We obtain the existence and multiplicity of one‐sign solutions for this problem and give the global structure of one‐sign solutions set according to different asymptotic behaviors of nonlinearity near zero.