Topological transversality. II: Applications to the Neumann problem for $$y''=f(t,y,y')$$.(English)Zbl 0534.34006

[For part I see ibid. 89, 53-67 (1980; Zbl 0453.34018).]
In this paper the Neumann problem for the nonlinear equation $$y''=f(t,y,y')$$ is studied. A priori bounds are derived and the results of Granas, Guenther and Lee, are invoked to obtain existence theorems. The existence theorems are in many cases quite different from those of the Dirichlet problem, e.g. it is possible to obtain general existence theorems where f(t,y,y’) can grow very rapidly in the y’ variable.

MSC:

 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems

Zbl 0453.34018
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