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INFINITELY MANY SOLUTIONS FOR NONLOCAL SYSTEMS INVOLVING FRACTIONAL LAPLACIAN UNDER NONCOMPACT SETTINGS
Published online by Cambridge University Press: 21 December 2018
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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- 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.