We consider the problem -Deltau = \u\(2*-2)u + lambdau in Omega, u = 0 on partial derivativeOmega, where Omega is an open regular subset of R-N (N greater than or equal to 3), 2* = 2N/N - 2 is the critical Sobolev exponent and lambda is a constant in]0, lambda(1)[ where lambda(1) is the first eigenvalue of -Delta. In this paper we show that, when N greater than or equal to 4, the problem has at least N/2 + 1 (pairs of) solutions, improving a result obtained in [4] for N greater than or equal to 6.
A multiplicity result for elliptic equations at critical growth in low dimension / Devillanova, G.; Solimini, S.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 5:2(2003), pp. 171-177. [10.1142/S0219199703000938]
A multiplicity result for elliptic equations at critical growth in low dimension
Devillanova, G.;Solimini, S.
2003-01-01
Abstract
We consider the problem -Deltau = \u\(2*-2)u + lambdau in Omega, u = 0 on partial derivativeOmega, where Omega is an open regular subset of R-N (N greater than or equal to 3), 2* = 2N/N - 2 is the critical Sobolev exponent and lambda is a constant in]0, lambda(1)[ where lambda(1) is the first eigenvalue of -Delta. In this paper we show that, when N greater than or equal to 4, the problem has at least N/2 + 1 (pairs of) solutions, improving a result obtained in [4] for N greater than or equal to 6.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
