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Remarks on least energy solutions for quasilinear elliptic problems in $$\mathbb R^N$$. (English) Zbl 1109.35318
The authors consider the quasilinear elliptic problem $-\Delta_p w= g(w),\quad\text{ in }\mathbb R^N,\tag{1}$ where $$\Delta_p u= \text{div}(|\nabla u|^{p-2}\nabla u)$$ is the $$p$$-Laplacian operator and $$1< p\leq N$$. Using variational methods more precisely by a constrained minimization argument, they show the existence of ground states solutions (or least energy solutions) for the (1) in both cases, $$1< p< N$$ and $$p= N$$. They prove also that the mountain-pass value gives the least energy level and obtain the exponential decay of the derivatives of the solutions of (1).

##### MSC:
 35J20 Variational methods for second-order elliptic equations 35J60 Nonlinear elliptic equations
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