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A barrier method for quasilinear ordinary differential equations of the curvature type. (English) Zbl 1046.34009
For equations of the form \[ \left (\frac {y'}{\sqrt {1+(y')^2}}\right)'=f(t,y), \] where \(f\) is continuous on \([a,\infty )\times \mathbb R\), the existence of a solution of the initial value problem \(y(a)=A\) is proved using the concept of sub- and supersolution. Examples are presented.

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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