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Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials
ID
Zhang, Xia
(
Author
),
ID
Zhang, Binlin
(
Author
),
ID
Repovš, Dušan
(
Author
)
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Abstract
This paper is concerned with the following fractional Schrödinger equations involving critical exponents: ▫$$(\Delta)^\alpha u + V(x)u = k(x)f(u) + \lambdau^{2_\alpha^\ast2}u \quad \text{in} \; \mathbb{R}^N,$$▫ where ▫$(\Delta)^\alpha$▫ is the fractional Laplacian operator with ▫$\alpha \in (0,1)$▫, ▫$N \ge 2$▫, ▫$\lambda$▫ is a positive real parameter and ▫$2_\alpha^\ast = 2N/(N2\alpha)$▫ is the critical Sobolev exponent, ▫$V(x)$▫ and ▫$k(x)$▫ are positive and bounded functions satisfying some extra hypotheses. Based on the principle of concentration compactness in the fractional Sobolev space and the minimax arguments, we obtain the existence of a nontrivial radially symmetric weak solution for the abovementioned equations without assuming the AmbrosettiRabinowitz condition on the subcritical nonlinearity.
Language:
English
Keywords:
fractional Schrödinger equations
,
critical Sobolev exponent
,
AmbrosettiRabinowitz condition
,
concentration compactness principle
Work type:
Article
Typology:
1.01  Original Scientific Article
Organization:
PEF  Faculty of Education
FMF  Faculty of Mathematics and Physics
Year:
2016
Number of pages:
Str. 4868
Numbering:
Vol. 142
PID:
20.500.12556/RUL111174
UDC:
517.95
ISSN on article:
0362546X
DOI:
http://dx.doi.org/10.1016/j.na.2016.04.012
COBISS.SIID:
17674585
Publication date in RUL:
25.09.2019
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1227
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535
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Record is a part of a journal
Title:
Nonlinear Analysis
Shortened title:
Nonlinear anal.
Publisher:
Pergamon Press
ISSN:
0362546X
COBISS.SIID:
26027520
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