Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 61, Issue 3, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-022-02221-8
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Funding
- NSFC [11971436, 12011530199]
- ZJNSF [LZ22A010001, LD19A010001]
- Romanian Ministry of Research, Innovation and Digitization, CNCS/CCCDI-UEFISCDI within PNCDI III [PCE 137/2021]
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In this paper, we study a weighted nonlocal system with critical exponents related to the Stein-Weiss inequality. By using moving plane arguments in integral form, we obtain symmetry, regularity and asymptotic properties, as well as sufficient conditions for the nonexistence of solutions to the nonlocal Stein-Weiss system.
In this paper, we study the following weighted nonlocal system with critical exponents related to the Stein-Weiss inequality {-Delta u = 1/vertical bar x vertical bar(alpha) (integral(RN) v(p)(y)/vertical bar x - y vertical bar(mu)vertical bar y vertical bar(alpha) dy) u(q), -Delta v = 1/vertical bar x vertical bar(alpha) (integral(RN) u(q) (y)/vertical bar x - y vertical bar(mu)vertical bar y vertical bar(alpha) dy) v(p), By using moving plane arguments in integral form, we obtain symmetry, regularity and asymptotic properties, as well as sufficient conditions for the nonexistence of solutions to the nonlocal Stein-Weiss system.
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