An eigenvalue problem for a quasilinear elliptic field equation on $\mathbb R^n$

Vieri Benci, Anna Maria Micheletti, Daniela Visetti

DOI: http://dx.doi.org/10.12775/TMNA.2001.013

Abstract


We study the field equation
$$-\Delta u+V(x)u+\varepsilon^r(-\Delta_pu+W'(u))=\mu u$$
on $\mathbb R^n$, with $\varepsilon$ 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 $\varepsilon$ sufficiently small, there
exists a finite number of solutions $(\mu(\varepsilon),u(\varepsilon))$
of the eigenvalue problem for any given charge $q\in{\mathbb Z}\setminus\{0\}$.

Keywords


Nonlinear systems; nonlinear Schrödinger equations; nonlinear eigenvalue problems

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