Vol. 71, No. 1, 1977

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Minimal and maximal solutions of nonlinear boundary value problems

Stephen Richard Bernfeld and Jagdish Chandra

Vol. 71 (1977), No. 1, 13–20
Abstract

This paper is concerned with the construction of the minimal and the maximal solutions of the nonlinear boundary value problem

u′′ = f (x,u,u′), 0 < x < 1

Biu = αiu(i)+ βiu′(i) = bi, i = 0,1

under rather mild assumptions on f. In particular, no assumption of monotonicity is made on f(x,u,u) either in u or u.

Mathematical Subject Classification 2000
Primary: 34B15
Milestones
Received: 14 September 1975
Published: 1 July 1977
Authors
Stephen Richard Bernfeld
Jagdish Chandra