Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

Abstract

Abstract We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation . Depending on the behaviour of f = f (t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.