In this paper we are concerned with a system of second-order differential equations of the form x'' + A(t, x)x = 0, t ∈ [0, T], x ∈ R^N, where A(t, x) is a symmetric N × N matrix. We concentrate on an asymptotically linear situation and we prove the existence of multiple solutions to the Dirichlet problem associated to the system. Multiplicity is obtained by a comparison between the number of moments of verticality of the matrices which are the uniform limits of A(t, x) for |x| → 0 and |x| → +∞, respectively. For the proof, which is based on a generalized shooting approach, we provide a theorem on the existence of zeros of a class of N-dimensional vector fields.
Scheda prodotto non validato
Scheda prodotto in fase di analisi da parte dello staff di validazione
|Titolo:||Detecting multiplicity for systems of second order equations: an alternative approach|
|Rivista:||ADVANCES IN DIFFERENTIAL EQUATIONS|
|Citazione:||Capietto, A., Dambrosio, W., & Papini, D. (2005). Detecting multiplicity for systems of second order equations: an alternative approach. ADVANCES IN DIFFERENTIAL EQUATIONS, 10(5), 553-578.|
|Appare nelle tipologie:||1.1 Articolo in rivista|