Let Ω be a C1 open bounded domain in ℝN, N ≥ 3, with (Formula presented.). We consider the following problem involving Hardy–Sobolev critical exponents: (Formula presented.), where 0 ≤ s1 < 2, 0 ≤ s2 < 2, 2 *(s2) ≠ λ ∈ ℝ, 1 ≤ p ≤ 2*(s1) - 1 and with choices of exponents and parameters corresponding to cases in which (P) has not been before investigated. We prove the existence of positive solutions, which, in some cases, are also shown to be ground states. We remark that we give a first partial answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3):943–968, 2012). © 2015, Springer-Verlag Berlin Heidelberg.
On some nonlinear PDEs with Sobolev-hardy critical exponents and a Li-Lin open problem / Cerami, Giovanna; Zhong, X; Zou, W.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 1432-0835. - 54:2(2015), pp. 1793-1829. [10.1007/s00526-015-0844-z]
On some nonlinear PDEs with Sobolev-hardy critical exponents and a Li-Lin open problem
CERAMI, Giovanna;
2015-01-01
Abstract
Let Ω be a C1 open bounded domain in ℝN, N ≥ 3, with (Formula presented.). We consider the following problem involving Hardy–Sobolev critical exponents: (Formula presented.), where 0 ≤ s1 < 2, 0 ≤ s2 < 2, 2 *(s2) ≠ λ ∈ ℝ, 1 ≤ p ≤ 2*(s1) - 1 and with choices of exponents and parameters corresponding to cases in which (P) has not been before investigated. We prove the existence of positive solutions, which, in some cases, are also shown to be ground states. We remark that we give a first partial answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3):943–968, 2012). © 2015, Springer-Verlag Berlin Heidelberg.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
