Please use this identifier to cite or link to this item: http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8065
Title: Existence and multiplicity of positive solutions of certain nonlocal scalar field equations
Authors: BHAKTA, MOUSOMI
CHAKRABORTY, SOUPTIK
Ganguly, Debdip
Dept. of Mathematics
Keywords: Energy estimate
Fractional Laplacian
Lusternik-Schnirelman category theory
Min-max method
Mountain-pass geometry
Nonlocal equations
Palais-Smale decomposition
Positive solutions
Scalar field equations
2023-JUN-WEEK4
TOC-JUN-2023
2023
Issue Date: Sep-2023
Publisher: Wiley
Citation: Mathematische Nachrichten, 296(09), 3816-3855.
Abstract: We study existence and multiplicity of positive solutions of the following class of nonlocal scalar field equations:.{(-Delta)(s) u +u =a (x)|u|(p-1)u +f (x) in R-N ( p), u is an element of H-s(R-N) where s is an element of (0,1), N> 2s, 1(s)(H) >= 0 whenever u is a nonnegative function in H-s (R-N). We establish Palais-Smale decomposition of the functional associated with the above equation. Using the decomposition, we establish existence of three positive solutions to (p), under the condition that a(x) <= 1 with a(x) -> 1 as |x|->infinity and parallel to f parallel to H (-s) (R-N) is small enough (but f not equivalent to 0). Further, we prove that (p) admits at least two positive solutions when a(x) >= 1, a(x)-> 1 as | x |->infinity and parallel to f parallel to H-s (R-N) is small enough (but f not equivalent to 0). Finally, we prove the existence of a positive solution when. f equivalent to 0 under certain asymptotic behavior on the function..
URI: https://doi.org/10.1002/mana.202000473
http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/8065
ISSN: 0025-584X
1522-2616
Appears in Collections:JOURNAL ARTICLES

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