On a biharmonic equation involving slightly supercritical exponent

@article{Bouh2018OnAB,
  title={On a biharmonic equation involving slightly supercritical exponent},
  author={Kamal Ould Bouh},
  journal={Turkish Journal of Mathematics},
  year={2018},
  volume={42}
}
  • K. Bouh
  • Published 24 March 2018
  • Mathematics
  • Turkish Journal of Mathematics
We consider the biharmonic equation with supercritical nonlinearity (Pε) : ∆ u = K|u|8/(n−4)+εu in Ω, ∆u = u = 0 on ∂Ω, where Ω is a smooth bounded domain in R , n ≥ 5, K is a C positive function, and ε is a positive real parameter. In contrast with the subcritical case, we prove the nonexistence of sign-changing solutions of (Pε) that blow up at two near points. We also show that (Pε) has no bubble-tower sign-changing solutions. 
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Sign-changing bubble tower solutions for a Paneitz-type problem
∆2u = |u| 8 N−4u in Ω\B(ξ0, ε), u = ∆u = 0 on ∂(Ω\B(ξ0, ε)), where Ω is an open bounded domain in R , N ≥ 5, and B(ξ0, ε) is a ball centered at ξ0 with radius ε, ε is a small positive parameter. We…

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