Bifurcation curves for the one-dimensional perturbed Gelfand problem with the Minkowski-curvature operator (Q6652150)

The authors studied the shapes of bifurcation curves of positive solutions for the one-dimensional perturbed Gelfand problem with the Minkowski-curvature operator \(-\big( u'(x)/\sqrt{1-|u'(x)|^2}\big)\) \(= \lambda \exp\Big(au/a+u\Big)\), \(-L<x<L\), \(u(-L)=u(L)=0\), where \(\lambda > 0\) is a bifurcation parameter and \(a,L > 0\) are evolution parameters. They determine the shapes of the bifurcation curves for different positive values \(a\) and \(L\). The main result generalises the main results in [\textit{S.-Y. Huang}, J. Differ. Equations 264, No. 9, 5977--6011 (2018; Zbl 1390.34051)].