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.
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.File in questo prodotto:
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