Weighted Sobolev embeddings and radial solutions of  inhomogeneous quasilinear elliptic equations

Jiabao Su; Rushun Tian

doi:10.3934/cpaa.2010.9.885

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2010, Volume 9, Issue 4: 885-904. Doi: 10.3934/cpaa.2010.9.885

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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

Received: June 30, 2009

Revised: October 31, 2009

Published: June 2010

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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.

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