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.


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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