scholarly journals Sign-Changing Solutions for a Fourth-Order Elliptic Equation with Hardy Singular Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Ruichang Pei ◽  
Jihui Zhang
Keyword(s):  
Elliptic Equation ◽  
Fourth Order ◽  
Elliptic Equations ◽  
Order Elliptic Equation ◽  
Singular Terms ◽  
Existence And Multiplicity ◽  
Minimax Methods ◽  
Fourth Order Elliptic Equation ◽  
Sign Changing Solutions

The existence and multiplicity of sign-changing solutions for a class of fourth elliptic equations with Hardy singular terms are established by using the minimax methods.

Fourth-order Elliptic Equations

2014 ◽  
Vol 14 (3) ◽  
Author(s):  
A. Harrabi
Keyword(s):  
Elliptic Equation ◽  
Fourth Order ◽  
Elliptic Equations ◽  
Existence Result ◽  
Order Elliptic Equation ◽  
Palais Smale Condition ◽  
Fourth Order Elliptic Equation ◽  
Fourth Order Elliptic Equations

AbstractWe prove an existence result for a fourth order elliptic equation where the associated functional does not satisfy the Palais-Smale condition. We use some truncations argument and L

scholarly journals On Fourth-Order Elliptic Equations of Kirchhoff Type with Dependence on the Gradient and the Laplacian

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yuanfang Ru ◽  
Fanglei Wang ◽  
Yunhai Wang ◽  
Tianqing An
Keyword(s):  
Elliptic Equation ◽  
Iterative Method ◽  
Nontrivial Solution ◽  
Fourth Order ◽  
Elliptic Equations ◽  
Mountain Pass Lemma ◽  
Order Elliptic Equation ◽  
Kirchhoff Type ◽  
Fourth Order Elliptic Equation ◽  
Fourth Order Elliptic Equations

We consider a nonlocal fourth-order elliptic equation of Kirchhoff type with dependence on the gradient and Laplacian Δ2u-a+b∫Ω∇u2dxΔu=fx,u,∇u,Δu, in Ω, u=0, Δu=0, on ∂Ω, where a, b are positive constants. We will show that there exists b⁎>0 such that the problem has a nontrivial solution for 0<b<b⁎ through an iterative method based on the mountain pass lemma and truncation method developed by De Figueiredo et al., 2004.

scholarly journals Embeddings of weighted Sobolev spaces and a weighted fourth-order elliptic equation

2019 ◽  
Vol 22 (06) ◽  
pp. 1950057
Author(s):  
Zongming Guo ◽  
Fangshu Wan ◽  
Liping Wang
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Sobolev Spaces ◽  
Weighted Sobolev Spaces ◽  
Order Elliptic Equation ◽  
Liouville Type ◽  
Related Equation ◽  
Fourth Order Elliptic Equation ◽  
Liouville Type Results

New embeddings of weighted Sobolev spaces are established. Using such embeddings, we obtain the existence and regularity of positive solutions with Navier boundary value problems for a weighted fourth-order elliptic equation. We also obtain Liouville type results for the related equation. Some problems are still open.

scholarly journals PRESCRIBING A FOURTH ORDER CONFORMAL INVARIANT ON THE STANDARD SPHERE — PART I: A PERTURBATION RESULT

2002 ◽  
Vol 04 (03) ◽  
pp. 375-408 ◽  
Author(s):  
ZINDINE DJADLI ◽  
ANDREA MALCHIODI ◽  
MOHAMEDEN OULD AHMEDOU
Keyword(s):  
Elliptic Equation ◽  
Fourth Order ◽  
Critical Sobolev Exponent ◽  
Order Elliptic Equation ◽  
Conformal Invariant ◽  
Standard Sphere ◽  
Finite Dimensional ◽  
Fourth Order Elliptic Equation ◽  
Zero Degree ◽  
Sobolev Exponent

In this paper we study some fourth order elliptic equation involving the critical Sobolev exponent, related to the prescription of a fourth order conformal invariant on the standard sphere. We use a topological method to prove the existence of at least a solution when the function to be prescribed is close to a constant and a finite dimensional map associated to it has non-zero degree

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