On the critical dimension of a fourth order elliptic problem with negative exponent

Abstract

We study the regularity of the extremal solution of the semilinear biharmonic equation β∆u−τ∆u = λ (1−u)2 on a ball B ⊂ R , under Navier boundary conditions u = ∆u = 0 on ∂B, where λ > 0 is a parameter, while τ > 0, β > 0 are fixed constants. It is known that there exists a λ∗ such that for λ > λ∗ there is no solution while for λ < λ∗ there is a branch of… (More)

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