The existence of eigenvalues for nonlinear homogeneous operators is discussed, considering perturbations of linear operators having a simple isolated eigenvalue. It is shown in particular that the nonlinear eigenvalues themselves are isolated. The proof is based on the Lyapounov-Schmidt reduction. The result is applied to a class of semilinear elliptic operators in bounded domains of R^n.
Chiappinelli, R. (2003). Isolated connected eigenvalues in nonlinear spectral theory. NONLINEAR FUNCTIONAL ANALYSIS AND APPLICATIONS, 8(4), 557-579.
Isolated connected eigenvalues in nonlinear spectral theory
CHIAPPINELLI, RAFFAELE
2003-01-01
Abstract
The existence of eigenvalues for nonlinear homogeneous operators is discussed, considering perturbations of linear operators having a simple isolated eigenvalue. It is shown in particular that the nonlinear eigenvalues themselves are isolated. The proof is based on the Lyapounov-Schmidt reduction. The result is applied to a class of semilinear elliptic operators in bounded domains of R^n.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/31105
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