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On the unique solvability of nonresonant elliptic equations. (English) Zbl 0603.35035
Problems of the type \(-\Delta u=g(x,u,\nabla u)\) in D, \(u=0\) on \(\partial D\) are considered where \[ \lambda_ k+\epsilon \leq [g(x,u_ 1,p)- g(x,u_ 2,p)]/(u_ 1-u_ 2)\leq \lambda_{k+1}+\epsilon \] , \(\lambda_ k\) being the kth eigenvalue of the Laplacian. By means of a contraction map it is shown that for functions g with linear growth in p the problem is uniquely solvable.
Reviewer: C.Bandle

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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