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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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