Abstract:We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential u). 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.

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation 8 > < > :where B R is a ball in R N (N ≥ 2). According to the behaviour of f = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

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