Vol. 74, No. 1, 1978

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A Nash-Moser-type implicit function theorem and nonlinear boundary value problems

Garo K. Kiremidjian

Vol. 74 (1978), No. 1, 105–132

The main objective of this paper is to formulate an implicit function theorem for Frechet spaces which is suitable for nonlinear systems of partial differential equations with prescribed boundary conditions. The applications are discussed in connection with deformation theory where such problems arise naturally and are of fundamental importance. Furthermore, their linearizations are certain second-order perturbations of second-order elliptic noncoercive boundary value problems. The last part of the paper deals with developing a general theory which covers these cases.

Mathematical Subject Classification 2000
Primary: 58C15
Secondary: 32G05
Received: 2 July 1976
Revised: 23 March 1977
Published: 1 January 1978
Garo K. Kiremidjian