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Multiplicity of Positive Solutions for a p - q -Laplacian Type Equation with Critical Nonlinearities
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-03
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We study the effect of the coefficient f ( x ) of the critical nonlinearity on the number of positive solutions for a p - q -Laplacian equation.
Under suitable assumptions for f ( x ) and g ( x ) , we should prove that for sufficiently small λ > 0 , there exist at least k positive solutions of the following p - q -Laplacian equation, - Δ p u - Δ q u = f x u | p * - 2 u + λ g x u | r - 2 u in Ω , u = 0 on ∂ Ω, where Ω ⊂ R N is a bounded smooth domain, N > p , 1 < q < N ( p - 1 ) / ( N - 1 ) < p ≤ max { p , p ^ * - q / ( p - 1 ) } < r < p ^ * , p ^ * = N p / ( N - p ) is the critical Sobolev exponent, and Δ s u = d i v ( | ∇ u | s - 2 ∇ u is the s -Laplacian of u .
American Psychological Association (APA)
Hsu, Tsing-San& Lin, Huei-li. 2014. Multiplicity of Positive Solutions for a p - q -Laplacian Type Equation with Critical Nonlinearities. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1014863
Modern Language Association (MLA)
Hsu, Tsing-San& Lin, Huei-li. Multiplicity of Positive Solutions for a p - q -Laplacian Type Equation with Critical Nonlinearities. Abstract and Applied Analysis No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-1014863
American Medical Association (AMA)
Hsu, Tsing-San& Lin, Huei-li. Multiplicity of Positive Solutions for a p - q -Laplacian Type Equation with Critical Nonlinearities. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1014863
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014863