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. 
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

References

SHOWING 1-10 OF 24 REFERENCES
Blowing up solutions for a biharmonic equation with critical nonlinearity
In this paper we consider the following biharmonic equation with critical exponent (P") : � 2 u = Ku n+4 n 4 −" , u > 0 in and u = �u = 0 on @, where is a smooth bounded domain in R n , n � 5, " is a
A NONEXISTENCE RESULT OF SINGLE PEAKED SOLUTIONS TO A SUPERCRITICAL NONLINEAR PROBLEM
This paper is concerned with the nonlinear elliptic problem (Pe): -Δu = up+e, u > 0 in Ω; u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝn, n ≥ 3, p + 1 = 2n/(n - 2) is the critical Sobolev
PROFILE AND EXISTENCE OF SIGN-CHANGING SOLUTIONS TO AN ELLIPTIC SUBCRITICAL EQUATION
In this paper, we study the nonlinear elliptic problem involving nearly critical exponent (Pe) : Δ2 u = |u|(8/(n-4))-eu, in Ω, Δu = u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝn, n ≥ 5. We
On a biharmonic equation involving nearly critical exponent
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 =
On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
Soit Ω un ensemble ouvert borne regulier et connexe de R N , N≥3. On considere u:Ω→R telle que −Δu=u (N+2)/(N−2) dans Ω, u>0 dans Ω, u=0 sur ∂Ω. On note par Hd(Ω; Z 2 ) l'homologie de diemnsion d de
Existence and nonexistence results for critical growth biharmonic elliptic equations
Abstract.We prove existence of nontrivial solutions to semilinear fourth order problems at critical growth in some contractible domains which are perturbations of small capacity of domains having
A note on additional properties of sign changing solutions to superlinear elliptic equations
We obtain upper bounds for the number of nodal domains of sign changing solutions of semilinear elliptic Dirichlet problems using suitable min-max descriptions. These are consequences of a
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