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Existence and symmetry of least energy solutions for a class of quasi-linear elliptic equations. (English) Zbl 1176.35081
Summary: For a general class of autonomous quasi-linear elliptic equations on $$\mathbb R^n$$ we prove the existence of a least energy solution and show that all least energy solutions do not change sign and are radially symmetric up to a translation in $$\mathbb R^n$$.

##### MSC:
 35J62 Quasilinear elliptic equations 35J40 Boundary value problems for higher-order elliptic equations 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 35B06 Symmetries, invariants, etc. in context of PDEs 35J35 Variational methods for higher-order elliptic equations
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