In this note we give some existence and nonexistence results of solutions to a problem of the type -div(vertical bar x vertical bar(-2 gamma) del u) = lambda/vertical bar x vertical bar(2(gamma+1)) u + u(p)/vertical bar x vertical bar(alpha) + f/vertical bar x vertical bar(2 gamma) in Omega u >= 0, u not equivalent to 0 in Omega (P-t,P-p) u = 0 on partial derivative Omega, where Omega is an open bounded subset of R-N containing the origin, the constants p, t. alpha, gamma, lambda satisfy suitable conditions and f not equivalent to 0 is a nonnegative, smooth bounded function on Omega. The results that will be given generalize some known results in Brezis et al. (2005) [1] and Dupaigne (2002) [2]. (C) 2012 Elsevier Inc. All rights reserved.
Semilinear elliptic equations with degenerate and singular weights related to Caffarelli-Kohn-Nirenberg inequalities
VOLZONE, Bruno
2012-01-01
Abstract
In this note we give some existence and nonexistence results of solutions to a problem of the type -div(vertical bar x vertical bar(-2 gamma) del u) = lambda/vertical bar x vertical bar(2(gamma+1)) u + u(p)/vertical bar x vertical bar(alpha) + f/vertical bar x vertical bar(2 gamma) in Omega u >= 0, u not equivalent to 0 in Omega (P-t,P-p) u = 0 on partial derivative Omega, where Omega is an open bounded subset of R-N containing the origin, the constants p, t. alpha, gamma, lambda satisfy suitable conditions and f not equivalent to 0 is a nonnegative, smooth bounded function on Omega. The results that will be given generalize some known results in Brezis et al. (2005) [1] and Dupaigne (2002) [2]. (C) 2012 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
