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Weighted Sobolev embedding with unbounded and decaying radial potentials. (English) Zbl 1220.35026
Summary: We prove embedding results of weighted $W^{1,p}(\Bbb R^N)$ spaces of radially symmetric functions. The results then are used to obtain ground and bound state solutions of quasilinear equations with unbounded or decaying radial potentials.

##### MSC:
 35J05 Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation 35J20 Second order elliptic equations, variational methods 35J60 Nonlinear elliptic equations
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##### References:
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