Nonlinear Elliptic Boundary Value Problems
نویسنده
چکیده
It is the object of the present note to present a new nonlinear version of the orthogonal projection method for proving the existence of solutions of nonlinear elliptic boundary value problems. The key point in this method is the application of a new general theorem concerning the solvability of nonlinear functional equations in a reflexive Banach space involving operators which may not be continuous. In several recent papers ([2], [3], [4], [5]) the writer obtained preliminary results in this direction involving operator equations in Hilbert space. The passage from Hilbert spaces to reflexive Banach spaces marks a tremendous increase in the power and applicability of this approach to nonlinear boundary value problems and involves a sharp development of its basic ideas. We show the existence of variational solutions of elliptic boundary value problems for strongly elliptic systems of order 2m on a domain in R in generalized divergence form
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