scholarly journals Existence and Multiplicity of Nodal Solutions for Nonlinear Elliptic Equations with Critical Sobolev Growth

1994 ◽  
Vol 119 (2) ◽  
pp. 298-318 ◽  
Author(s):  
E. Hebey ◽  
M. Vaugon
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Nodal Solutions ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

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.

Nonexistence of nodal solutions of nonlinear elliptic equations

2001 ◽  
Vol 46 (8) ◽  
pp. 1111-1122 ◽  
Author(s):  
Soohyun Bae ◽  
Dae Hyeon Pahk
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Nodal Solutions ◽  
Nonlinear Elliptic

Multiple Positive Solutions For a Class of Nonlinear Elliptic Equations

2006 ◽  
Vol 6 (1) ◽  
Author(s):  
Shenghua Weng ◽  
Yongqing Li
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Nonlinear Elliptic Equations ◽  
Multiple Positive Solutions ◽  
Combined Effects ◽  
Multiplicity Results ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

AbstractThis paper deals with a class of nonlinear elliptic Dirichlet boundary value problems where the combined effects of a sublinear and a superlinear term allow us to establish some existence and multiplicity results.

Nodal solutions for some nonlinear elliptic equations

2007 ◽  
Vol 186 (1) ◽  
pp. 589-597 ◽  
Author(s):  
Anouar Ben Mabrouk ◽  
Mohamed Lakdar Ben Mohamed
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Nodal Solutions ◽  
Nonlinear Elliptic

scholarly journals Constant sign and nodal solutions for nonlinear elliptic equations with combined nonlinearities

2015 ◽  
Vol 22 (2) ◽  
pp. 221-248
Author(s):  
Sergiu Aizicovici ◽  
Nikolaos S. Papageorgiou ◽  
Vasile Staicu
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Constant Sign ◽  
Nodal Solutions ◽  
Nonlinear Elliptic
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