Bifurcation curves of positive solutions for one-dimensional Minkowski curvature problem

Abstract

In this paper, we study the shape of the bifurcation curves of positive solutions for the one-dimensional Minkowski-curvature problem. By developing some new time mapping techniques, we find that the bifurcation curve is ⊂-shaped/monotone increasing/S-like shaped on the (λ,||u||∞) plane when the nonlinearity satisfies different assumptions. Finally, two examples are given to illustrate our result.

Keywords

• mean curvature equation
• positive solutions
• bifurcation curve
• time mapping
• existence