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On semilinear elliptic eigenvalue problem with eigenparameter in the boundary conditions. (English) Zbl 1090.35078
Summary: The object of this paper is to establish the expansion theorem for a semilinear elliptic eigenvalue problem of a simply connected bounded domain in \(R^n\) \((n\geq 2)\), where the eigenvalue parameter \(\lambda\) is contained in the semilinear elliptic partial differential equation and in the boundary conditions. We associated with this problem a semilinear selfadjoint operator \(S\) in a suitably defined Hilbert space \(H\) and then we develop an associated eigenfunction expansion theorem.
MSC:
35J60 Nonlinear elliptic equations
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
47F05 General theory of partial differential operators
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