Abstract
The purpose of this paper is to discuss non-linear boundary value problems for elliptic systems of the typewhere Ak is a second order uniformly elliptic operator and is such that the problemhas a one-dimensional space of solutions that is generated by a non-negative function. The boundary ∂G is supposed to be smooth and the functions gk, 1≦k≦m are defined on Ḡ×Rm and are continuously differentiate (usually, Bk represents Dirichlet or Neumann conditions and is the first eigenvalue associated with Ak and such boundary conditions).
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