Abstract
In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic equation with Sobolev critical exponent in a bounded domain. By using the idea of the previous paper, we generalize the results and prove the existence and multiplicity of nontrivial solutions of the biharmonic elliptic equations.
Highlights
Introduction and Main ResultsIn the present paper, we are concerned with the existence of multiple solutions to the following biharmonic elliptic equation with perturbationΔ2u = |u|p−2 u + f, x ∈ Ω, (1)u = ∇u = 0, x ∈ ∂Ω, where Ω is a bounded domain in RN (N ≥ 5), Δ2 is the biharmonic operator, and p = 2∗∗ = 2N/(N − 4) is the Sobolev critical exponent.The second-order semilinear and quasilinear problems have been object of intensive research in the last years
We study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic equation with Sobolev critical exponent in a bounded domain
We are concerned with the existence of multiple solutions to the following biharmonic elliptic equation with perturbation
Summary
We are concerned with the existence of multiple solutions to the following biharmonic elliptic equation with perturbation. If λ > 0 and Ω is a ball, paper [13] proved the existence of positive radially symmetric solutions. We shall generalize the results of Tarantello [22] to the biharmonic and critical exponent case. −a) and out that tξhae∈emC∞ 0be(dΩd)inwgitDh ξa→≥L0pa(Ωnd) is not compact This leads to the lack of compactness for the proved existence and multiplicity of nontrivial solutions of (1). It is clear that all critical points lie in the Nehari manifold, and it is usually effective to consider the existence of critical points in this smaller subset of the Sobolev space. U0 is a critical point of I, and u0 ≥ 0 when f ≥ 0 In this case we have the following results. The proofs of Theorems 1–2 rely on the Ekeland’s variational principle and careful estimates (see [1]) of minimizing sequence
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