We discuss the equation (1) F(u)≡Tu+N(u)=λu, where T is a compact selfadjoint linear operator, the nonlinear perturbation N:H→H is assumed to be a positively homogeneous and completely continuous gradient operator. We discuss the existence and location of eigenvalues of F , bifurcating from unperturbed eigenvalues of T. The critical points theory of smooth functionals is used.
Chiappinelli, R. (2001). On the eigenvalue problem for some nonlinear perturbations of compact selfadjoint operators. PDF Clipboard Journal Article. NONLINEAR ANALYSIS FORUM, 6(1), 69-77.
On the eigenvalue problem for some nonlinear perturbations of compact selfadjoint operators. PDF Clipboard Journal Article
CHIAPPINELLI, RAFFAELE
2001-01-01
Abstract
We discuss the equation (1) F(u)≡Tu+N(u)=λu, where T is a compact selfadjoint linear operator, the nonlinear perturbation N:H→H is assumed to be a positively homogeneous and completely continuous gradient operator. We discuss the existence and location of eigenvalues of F , bifurcating from unperturbed eigenvalues of T. The critical points theory of smooth functionals is used.
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https://hdl.handle.net/11365/32679
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