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

  • M. KHIDDI (a1), S. BENMOULOUD (a2) and S. M. SBAI (a3)
Abstract

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.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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