Ibrahim, S. F. M. On semilinear elliptic eigenvalue problem with eigenparameter in the boundary conditions. (English) Zbl 1090.35078 Southwest J. Pure Appl. Math. 2002, No. 2, 68-76 (2002). 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 Keywords:semilinear elliptic eigenvalue problem; eigenvalue parameter in boundary conditions; semilinear operator; Hilbert space formulation; eigenfunction expansion theorem PDFBibTeX XMLCite \textit{S. F. M. Ibrahim}, Southwest J. Pure Appl. Math. 2002, No. 2, 68--76 (2002; Zbl 1090.35078) Full Text: EuDML EMIS