Geodesic
On Jost-Type Solutions to Quasilinear Equations with Power Nonlinearity
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 332-337

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By a variant of the WKB method, Jost-type solutions are constructed for second-order quasilinear ordinary differential equations with power nonlinearity. By an example of the second Painlevé equation, it is demonstrated that the existence conditions obtained for the above solutions are sharp in a certain sense. 
@article{TM_2002_236_a33,
     author = {S. A. Stepin},
     title = {On {Jost-Type} {Solutions} to {Quasilinear} {Equations} with {Power} {Nonlinearity}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {332--337},
     publisher = {mathdoc},
     volume = {236},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_236_a33/}
}
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S. A. Stepin. On Jost-Type Solutions to Quasilinear Equations with Power Nonlinearity. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 332-337. http://geodesic.mathdoc.fr/item/TM_2002_236_a33/