Nontrivial solutions to semilinear elliptic problems involving two critical Hardy–Sobolev exponents

Nontrivial solutions to semilinear elliptic problems involving two critical Hardy–Sobolev exponents

In this paper, we investigate a semilinear elliptic equation, which involves doubly critical Hardy–Sobolev exponents and a Hardy-type term. By means of the Linking Theorem and delicate energy estimates, the existence of nontrivial solutions to the problem is established.

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Veröffentlicht in:Nonlinear analysis 2010-06, Vol.72 (11), p.4230-4243
1. Verfasser: Kang, Dongsheng
Format: Artikel
Sprache:eng
Schlagworte:
Critical exponent
Estimates
Exact sciences and technology
Existence theorems
Exponents
Hardy–Sobolev inequality
Joining
Linking
Mathematical analysis
Mathematics
Nonlinearity
Partial differential equations
Sciences and techniques of general use
Semilinear equation
Singularity
Solution
Theorems
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Beschreibung
Zusammenfassung:In this paper, we investigate a semilinear elliptic equation, which involves doubly critical Hardy–Sobolev exponents and a Hardy-type term. By means of the Linking Theorem and delicate energy estimates, the existence of nontrivial solutions to the problem is established.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2010.01.053