Variational Methods for NLEV Approximation Near a Bifurcation Point | Zendy

Raffaele Chiappinelli | Zendy

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Variational Methods for NLEV Approximation Near a Bifurcation Point

Author(s) -

Raffaele Chiappinelli

Publication year - 2012

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2012/102489

Subject(s) - mathematics , eigenvalues and eigenvectors , bifurcation theory , hilbert space , bounded function , norm (philosophy) , nonlinear system , bifurcation , mathematical analysis , pure mathematics , physics , quantum mechanics , political science , law

We review some more and less recent results concerning bounds on nonlinear eigenvalues (NLEV) for gradient operators. In particular, we discuss the asymptotic behaviour of NLEV (as the norm of the eigenvector tends to zero) in bifurcation problems from the line of trivial solutions, considering perturbations of linear self-adjoint operators in a Hilbert space. The proofs are based on the Lusternik-Schnirelmann theory of critical points on one side and on the Lyapounov-Schmidt reduction to the relevant finite-dimensional kernel on the other side. The results are applied to some semilinear elliptic operators in bounded domains of . A section reviewing some general facts about eigenvalues of linear and nonlinear operators is included

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