Topological transversality. II. Applications to the Neumann problem for y^′′ = f(t, y, y^′)

Andrzej Granas, Ronald Bernard Guenther and John Walter Lee

Vol. 104 (1983), No. 1, 95–109

DOI: 10.2140/pjm.1983.104.95

Abstract

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.

Mathematical Subject Classification 2000

Primary: 34B15

Milestones

Received: 9 May 1980

Published: 1 January 1983