2011
DOI: 10.1016/j.jde.2010.08.025
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Sobolev type embedding and quasilinear elliptic equations with radial potentials

Abstract: MSC: 35J05 35J20 35J60 58C20 Keywords: Quasilinear elliptic equations Unbounded or decaying potentials Sobolev type embeddingWe study the existence of nontrivial radial solutions for quasilinear elliptic equations with unbounded or decaying radial potentials. The existence results are based upon several new embedding theorems we establish in the paper for radially symmetric functions.

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Cited by 49 publications
(43 citation statements)
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“…Remark This version of radial inequality was given in and its proof is similar to Lemma 1 in , which was for l=0. The case l=0,p=2 is known as Ni's inequality .…”
Section: Imbedding Resultsmentioning
confidence: 91%
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“…Remark This version of radial inequality was given in and its proof is similar to Lemma 1 in , which was for l=0. The case l=0,p=2 is known as Ni's inequality .…”
Section: Imbedding Resultsmentioning
confidence: 91%
“…We begin with two radial inequalities, which are essential tools in our arguments. Lemma ( ) Let lR be such that 1<p<N+l. Then there exists C>0 such that for all uDr1,pRN;|x|l, the completion of C0,rRN under uDr1,p(boldRN;|x|l)=()boldRN|x|l|u|p0.33emdx1p,it holds that |u(x)|C|x|N+lppuDr1,p(boldRN;|x|l).…”
Section: Imbedding Resultsmentioning
confidence: 99%
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“…Besides, we also mention that when μ = s = 0 and the right-hand side term |x| −s u 2 * (s)−1 is replaced by u q−1 (1 < q < 2N N−2 or q = 2N N−2 ) in (1.2), some elegant results of G-symmetric solutions of (1.2) were established in [10][11][12]. Finally, when G = O(N), we remark that Su and Wang [13] proved the existence of nontrivial radial solutions for a class of quasilinear singular equations such as (1.2) with radial potentials by establishing several new embedding theorems.…”
Section: Introductionmentioning
confidence: 75%
“…Such kind of embeddings of weighted Sobolev spaces with different weights have been studied by some authors, see . Especially, some results of embeddings with power weights in RN or boldRN{0} can be found in .…”
Section: Introductionmentioning
confidence: 99%