# Asymptotics of positive solutions for a biharmonic equation involving critical exponent

@article{Chou2000AsymptoticsOP, title={Asymptotics of positive solutions for a biharmonic equation involving critical exponent}, author={Kai-Seng Chou and Di Geng}, journal={Differential and Integral Equations}, year={2000}, volume={13}, pages={921-940} }

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## 32 Citations

Asymptotic behavior of least energy solutions to the Lane-Emden system near the critical hyperbola

- Mathematics
- 2018

Asymptotic Uniqueness for a Biharmonic Equation with Nearly Critical Growth on Symmetric Convex Domains

- Mathematics
- 2009

We consider a biharmonic equation with the nearly critical Sobolev exponent under the Navier boundary condition on a smooth bounded, strictly convex domain of dimension N ≥ 5, which is symmetric with…

Asymptotic behavior of least energy solutions for a biharmonic problem with nearly critical growth

- MathematicsAsymptot. Anal.
- 2008

B boundary condition of (Pε,K) is called as the Navier boundary condition for the second-order Laplacian-case problem ⎧⎨ ⎩ −Δu = N (N − 2)K(x)u(N+2)/(N −2)−ε in Ω, u = 0 on ∂Ω.

On a biharmonic equation involving nearly critical exponent

- Mathematics
- 2004

Abstract.This paper is concerned with a biharmonic equation under the Navier boundary condition
$${(P_{\mp\varepsilon}): \Delta^{2}u = u^{\frac{n+4}{n-4}\mp\varepsilon}}$$
, u > 0 in Ω and u = Δu =…

Minimal energy solutions to the fractional Lane–Emden system: Existence and singularity formation

- MathematicsRevista Matemática Iberoamericana
- 2019

This is the first of two papers which study asymptotic behavior of minimal energy solutions to the fractional Lane-Emden system in a smooth bounded domain $\Omega$ \[(-\Delta)^s u = v^p, \quad…

Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces

- Mathematics
- 2013

We obtain an improved Sobolev inequality in $$\dot{H}^s$$H˙s spaces involving Morrey norms. This refinement yields a direct proof of the existence of optimizers and the compactness up to symmetry of…

Sign-changing bubble tower solutions for a Paneitz-type problem

- Mathematics
- 2022

∆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…

Sign-changing tower of bubbles to an elliptic subcritical equation

- Mathematics, ArtCommunications in Contemporary Mathematics
- 2019

This paper is concerned with the following nonlinear elliptic problem involving nearly critical exponent [Formula: see text]: [Formula: see text] in [Formula: see text], [Formula: see text] on…

On a biharmonic equation involving slightly supercritical exponent

- Mathematics
- 2018

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,…