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Advisor(s)
Abstract(s)
We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, 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.
Description
Keywords
Quasilinear Ordinary Differential Equation Minkowski-Curvature Dirichlet Boundary Conditions Positive Solution Existence Multiplicity Critical Point Theory Bifurcation Methods Lower and Upper Solutions
Citation
Coelho I, Corsato C, Obersnel F, Omari P. Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation. Advanced Nonlinear Studies. 2012; 3 (12): 621-638.