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INFINITELY MANY SOLUTIONS FOR NONLOCAL SYSTEMS INVOLVING FRACTIONAL LAPLACIAN UNDER NONCOMPACT SETTINGS

Part of: Elliptic equations and systems Existence theories Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  21 December 2018

M. KHIDDI Open the ORCID record for M. KHIDDI [Opens in a new window] ,
S. BENMOULOUD  and
S. M. SBAI
M. KHIDDI*
Affiliation:
E.G.A.L., Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail, BP 133, Kénitra, Morocco email mostapha-2@hotmail.com
S. BENMOULOUD
Affiliation:
E.G.A.L., Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail, BP 133, Kénitra, Morocco
S. M. SBAI
Affiliation:
E.G.A.L., Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail, BP 133, Kénitra, Morocco
*
✉mostapha-2@hotmail.com
Rights & Permissions [Opens in a new window]

Abstract

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In this paper, we study a class of Brezis–Nirenberg problems for nonlocal systems, involving the fractional Laplacian $(-\unicode[STIX]{x1D6E5})^{s}$ operator, for $0<s<1$, posed on settings in which Sobolev trace embedding is noncompact. We prove the existence of infinitely many solutions in large dimension, namely when $N>6s$, by employing critical point theory and concentration estimates.

Keywords

critical point

MSC classification

Primary: 35J60: Nonlinear elliptic equations
Secondary: 49J35: Minimax problems 35R11: Fractional partial differential equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 107 , Issue 2 , October 2019 , pp. 215 - 233
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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