The existence of solutions to the problem -Δu - λu = u|u|2* - 2 in Ωu|∂Ω = 0 is studied. For an arbitrary domain Ω ⊂Rn, if λ ε{lunate} ]0, λ1[ and n ≥ 6, the existence of solutions of changing sign is obtained. If Ω = BR(0) ⊂ Rn, λ ε{lunate} ]0, λ1[, and n ≥ 7, infinitely many radial solutions to this problem are exhibited, characterized by the number of nodes they possess.
Some existence results for superlinear elliptic boundary value problems involving critical exponents / Cerami, G.; Solimini, S.; Struwe, M.. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 69:3(1986), pp. 289-308. [10.1016/0022-1236(86)90094-7]
Some existence results for superlinear elliptic boundary value problems involving critical exponents
Cerami, G.;Solimini, S.;
1986-01-01
Abstract
The existence of solutions to the problem -Δu - λu = u|u|2* - 2 in Ωu|∂Ω = 0 is studied. For an arbitrary domain Ω ⊂Rn, if λ ε{lunate} ]0, λ1[ and n ≥ 6, the existence of solutions of changing sign is obtained. If Ω = BR(0) ⊂ Rn, λ ε{lunate} ]0, λ1[, and n ≥ 7, infinitely many radial solutions to this problem are exhibited, characterized by the number of nodes they possess.File in questo prodotto:
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