scholarly journals On the Sets of Regularity of Solutions for a Class of Degenerate Nonlinear Elliptic Fourth-Order Equations with L1 Data

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
S. Bonafede ◽  
F. Nicolosi
Keyword(s):  
Fourth Order ◽  
Regularity Of Solutions ◽  
Nonlinear Elliptic ◽  
L1 Data ◽  
Fourth Order Equations

Summability of solutions of some degenerate nonlinear elliptic fourth-order equations

2005 ◽  
Vol 84 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Alexander Kovalevsky ◽  
Francesco Nicolosi ‡
Keyword(s):  
Fourth Order ◽  
Nonlinear Elliptic ◽  
Fourth Order Equations

ON A CLASS OF FOURTH ORDER NONLINEAR ELLIPTIC EQUATIONS UNDER NAVIER BOUNDARY CONDITIONS

2010 ◽  
Vol 08 (02) ◽  
pp. 185-197 ◽  
Author(s):  
F. J. S. A. CORRÊA ◽  
J. V. GONCALVES ◽  
ANGELO RONCALLI
Keyword(s):  
Boundary Conditions ◽  
Fixed Points ◽  
Fourth Order ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Compact Operators ◽  
Schmidt Method ◽  
Navier Boundary Conditions ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

We employ arguments involving continua of fixed points of suitable nonlinear compact operators and the Lyapunov–Schmidt method to prove existence and multiplicity of solutions in a class of fourth order non-homogeneous resonant elliptic problems. Our main result extends even similar ones known for the Laplacian.

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