Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints

1989 ◽  
Vol 283 (4) ◽  
pp. 583-630 ◽  
Author(s):  
J. M. Lasry ◽  
P. L. Lions
Keyword(s):  
Boundary Conditions ◽  
Stochastic Control ◽  
Elliptic Equations ◽  
State Constraints ◽  
Nonlinear Elliptic Equations ◽  
Singular Boundary ◽  
Nonlinear Elliptic

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.

scholarly journals Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions

2019 ◽  
Vol 39 (2) ◽  
pp. 159-174 ◽  
Author(s):  
Gabriele Bonanno ◽  
Giuseppina D'Aguì ◽  
Angela Sciammetta
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Mixed Boundary ◽  
Neumann Boundary ◽  
Nonlinear Elliptic Equations ◽  
Mixed Boundary Conditions ◽  
Neumann Boundary Conditions ◽  
Laplacian Operator ◽  
Differential Problem ◽  
Nonlinear Elliptic

In this paper, a nonlinear differential problem involving the \(p\)-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results.

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