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neralized Euler-Lagrange equation. In this paper we propose a Newton-like method and show that this proposed method is general enough to enable us to construct solutions of the generalized Euler-Lagrange equation. Let X and Y be Banach spaces, Ω an open subset of X and P: Ω—+Y. By [X, Y] we mean the Banach space of all bounded linear operators with the usual operator norm, by P ' the first derivative of P and by P" the second derivative of P. The class of all functions defined on Ω which have continuous derivatives up to and including order n at each point of Ω is denoted by C(Ω). Distinct elements of C(Ω) may have totally distinct ranges depending on the application. The distinction between Gateaux and Frechet is unnecessary since the derivatives will be continuous.

An application of a Newton-like method to the Euler-Lagrange equation