Evolution of bifurcation curves for one-dimensional Minkowski-curvature problem

This paper is concerned with the Robin problem for the prescribed mean curvature equation in Minkowski space -(u'/root 1-|u'|2)'=0u(q)+mu up,t0(0,L),u'(0)=u(L)=0,(P) where 0<q<1<(p). We show that there exists a constant mu*>0 and two functions 0*(center dot),0*(center dot) with 0*(mu)<lambda<lambda*(mu),mu>mu*, such that for every mu>mu* and all lambda(0*(mu),0), (P) has at least two positive solutions; for every mu>mu* and all 00(0,0*(mu)), (P) has at least three positive solutions. The proof combines topological degree and bifurcation technique. We also present a numerical computation of the bifurcation curves. (C) 2019 Elsevier Ltd. All rights reserved.