One-dimensional prescribed mean curvature equation with exponential nonlinearity

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Positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space (2013, unknown): “The one-dimensional problem has been rather thoroughly discussed in a series of recent papers by Bonheure, Habets, Obersnel and Omari [23, 5, 36, 6], Bereanu and Mawhin [4] and Pan [40].”
Positive solutions of the Dirichlet problem for the prescribed mean curvature equation (2010, background): “The one-dimensional problem has been rather thoroughly discussed in a series of recent papers by Bonheure, Habets, Obersnel and Omari [23, 5, 36, 6], Bereanu and Mawhin [4] and Pan [40].”