In this paper, we consider the problem -Δu = |u|2*-2u+λu in ω, u = 0 on ∂ω, where ω is an open regular bounded subset of ℝN (N ≥3), 2* = 2N/N-2 is the critical Sobolev exponent and λ> 0. Our main result asserts that, if N ≥7, the problem has infinitely many solutions and, from the point of view of the compactness arguments employed here, the restriction on the dimension N cannot be weakened.

Concentration estimates and multiple solutions to elliptic problems at critical growth / Devillanova, Giuseppe; Solimini, Sergio Fausto. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 7:10(2002), pp. 1257-1280.

Concentration estimates and multiple solutions to elliptic problems at critical growth

Devillanova, Giuseppe;Solimini, Sergio Fausto
2002-01-01

Abstract

In this paper, we consider the problem -Δu = |u|2*-2u+λu in ω, u = 0 on ∂ω, where ω is an open regular bounded subset of ℝN (N ≥3), 2* = 2N/N-2 is the critical Sobolev exponent and λ> 0. Our main result asserts that, if N ≥7, the problem has infinitely many solutions and, from the point of view of the compactness arguments employed here, the restriction on the dimension N cannot be weakened.
2002
Concentration estimates and multiple solutions to elliptic problems at critical growth / Devillanova, Giuseppe; Solimini, Sergio Fausto. - In: ADVANCES IN DIFFERENTIAL EQUATIONS. - ISSN 1079-9389. - STAMPA. - 7:10(2002), pp. 1257-1280.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/11623
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