Liouville-type results for fourth order elliptic equations

1986 ◽  
Vol 103 (3-4) ◽  
pp. 209-213 ◽  
Author(s):  
Vinod B. Goyal
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Liouville Type ◽  
Liouville Type Theorems ◽  
Liouville Type Results ◽  
Fourth Order Elliptic Equations

SynopsisLiouville type theorems are obtained for the solutions to elliptic equations of the form Δ2u −q(x)Δu + p(x)f(u)=0 by means of two subharmonic functionals and Green type inequalities.

Liouville theorems for a class of fourth order elliptic equations

1980 ◽  
Vol 86 (1-2) ◽  
pp. 129-137 ◽  
Author(s):  
Vinod B. Goyal ◽  
Philip W. Schaefer
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Entire Solutions ◽  
Liouville Type ◽  
Liouville Theorems ◽  
Liouville Type Theorems ◽  
Solutions Of Equations ◽  
Fourth Order Elliptic Equations

SynopsisLiouville type theorems are obtained for bounded entire solutions of equations of the form Δ2u − q(x)Δu + p(x)u = 0 by means of subharmonic functionals and Green type inequalities.

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.

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