Abstract
We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation
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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.
Keywords: Quasilinear ordinary differential equation; Minkowski-curvature; Dirichlet boundary conditions; positive solution; existence; multiplicity; critical point theory; bifurcation methods; lower and upper solutions
Published Online: 2016-03-10
Published in Print: 2012-08-01
© 2016 by Advanced Nonlinear Studies, Inc.
