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 $qin{mathbb Z}setminus{0}$.
Articolo in rivista - Articolo scientifico
Nonlinear systems, nonlinear Schrödinger equations, nonlinear eigenvalue problems;
English
191
211
21
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/350964
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