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Communications on Pure and Applied Analysis (CPAA)
 

Weighted Sobolev embeddings and radial solutions of inhomogeneous quasilinear elliptic equations

Pages: 885 - 904, Volume 9, Issue 4, July 2010

doi:10.3934/cpaa.2010.9.885       Abstract        Full Text (268.1K)       Related Articles

Jiabao Su - School of Mathematical Sciences, Capital Normal University, Beijing 100048, China (email)
Rushun Tian - School of Mathematical Sciences, Capital Normal University, Beijing 100048, China (email)

Abstract: 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, 58C20.

Received: July 2009;      Revised: November 2009;      Published: April 2010.