Sign-changing solutions for fourth-order elliptic equations of Kirchhoff type with critical exponent

Sihua Liang,Binlin Zhang

doi:10.14232/ejqtde.2021.1.37

Abstract

Sign-changing solutions for fourth-order elliptic equations of Kirchhoff type with critical exponent

Highlights

Introduction and main resultsIn this paper, we are interested in the existence of least energy nodal solutions for the following Kirchhoff-type fourth-order Laplacian equations with critical growth:u = ∆u = 0 on ∂Ω, (1.1)where ∆2 is the biharmonic operator, N = {5, 6, 7}, 2∗∗ = 2N/(N − 4) is the Sobolev critical exponent, Ω ⊂ RN is an open bounded domain with smooth boundary, and b, λ are some positive parameters.S
We are interested in the existence of least energy nodal solutions for the following Kirchhoff-type fourth-order Laplacian equations with critical growth:
In [33], the authors obtained the existence of least energy sign-changing solutions of Kirchhoff-type equation with critical growth by using the constraint variational method and the quantitative deformation lemma

Summary

Introduction

There is a vast literature concerning the existence and multiplicity of solutions for the following Dirichlet problem of Kirchhoff type U = ∆u = 0, x ∈ ∂Ω, and obtained the existence and multiplicity of solutions, see [19, 20, 34] for more results. In [30], Song and Shi obtained the existence and multiplicity of solutions for problem (1.6) critical exponent in bounded domains by using the concentration-compactness principle and variational method.

Objectives

Results

Conclusion