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July  2010, 9(4): 885-904. doi: 10.3934/cpaa.2010.9.885

Weighted Sobolev embeddings and radial solutions of inhomogeneous quasilinear elliptic equations

Jiabao Su 1, and  Rushun Tian 1,

1. 

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

Received  July 2009 Revised  November 2009 Published  April 2010

We study weighted Sobolev embeddings in radially symmetric function spaces and then investigate the existence of nontrivial radial solutions of inhomogeneous quasilinear elliptic equation with singular potentials and super-$(p, q)$-linear nonlinearity. The model equation is of the form

$ -\Delta_p u+V(|x|)|u|^{q-2}u=Q(|x|)|u|^{s-2}u, x\in R^N,$

$ u(x) \rightarrow 0,$ as $ |x|\rightarrow\infty. $

Keywords: Inhomogeneous quasilinear elliptic equation, Sobolev type embedding..
Mathematics Subject Classification: 35J05, 35J20, 35J60, 58C2.
Citation: Jiabao Su, Rushun Tian. Weighted Sobolev embeddings and radial solutions of inhomogeneous quasilinear elliptic equations. Communications on Pure and Applied Analysis, 2010, 9 (4) : 885-904. doi: 10.3934/cpaa.2010.9.885
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