We study the field equation $$-Delta u+V(x)u+arepsilon^r(-Delta_pu+W'(u))=mu u$$ on $mathbb R^n$, with $arepsilon$ positive parameter. The function $W$ is singular in a point and so the configurations are characterized by a topological invariant: the topological charge. By a min-max method, for $arepsilon$ sufficiently small, there exists a finite number of solutions $(mu(arepsilon),u(arepsilon))$ of the eigenvalue problem for any given charge $qin{mathbb Z}setminus{0}$.
Benci, V., Micheletti, A., Visetti, D. (2001). An eigenvalue problem for a quasilinear elliptic field equation on R^n. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 17(2), 191-211 [10.12775/TMNA.2001.013].
An eigenvalue problem for a quasilinear elliptic field equation on R^n
Benci V;
2001
Abstract
We study the field equation $$-Delta u+V(x)u+arepsilon^r(-Delta_pu+W'(u))=mu u$$ on $mathbb R^n$, with $arepsilon$ positive parameter. The function $W$ is singular in a point and so the configurations are characterized by a topological invariant: the topological charge. By a min-max method, for $arepsilon$ sufficiently small, there exists a finite number of solutions $(mu(arepsilon),u(arepsilon))$ of the eigenvalue problem for any given charge $qin{mathbb Z}setminus{0}$.
| File | Dimensione | Formato | |
|---|---|---|---|
|
1_bmv_tmna.pdf
Solo gestori archivio
Tipologia di allegato:
Publisher’s Version (Version of Record, VoR)
Licenza:
Tutti i diritti riservati
Dimensione
282.86 kB
Formato
Adobe PDF
|
282.86 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
