Let Ω⊂R N (N>2) be a bounded open set with smooth boundary ∂Ω , and letv L_0 be a uniformly elliptic operator acting in the Sobolev space H 1 0 (Ω) . Denote by (μ 0 n) the sequence of eigenvalues of the problem L_0 u=μu in Ω, u=0 on ∂Ω . The purpose of this paper is to study the stability of an eigenvalue μ 0 n (n fixed), under addition to L_0 of a nonlinear term of the form m(x,s) , under various conditions on the function m:Ω×R→R . We establish bounds on the perturbed eigenvalue μ r (associated with eigenfunctions u with ∥u∥ L 2 (Ω) =r) , and discuss the connection with bifurcation from the trivial solutions.
|Titolo:||Constrained critical points and eigenvalue approximation for semilinear elliptic operators|
|Citazione:||Chiappinelli, R. (1999). Constrained critical points and eigenvalue approximation for semilinear elliptic operators. FORUM MATHEMATICUM, 11(4), 459-481.|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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