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 $q\in{\mathbb Z}\setminus\{0\}$.
Citation
V. Benci. A. M. Micheletti. D. Visetti. "An eigenvalue problem for a quasilinear elliptic field equation on $\mathbb R^n$." Topol. Methods Nonlinear Anal. 17 (2) 191 - 211, 2001.
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