Extremal solutions of -Laplacian–diffusion scalar problems with nonlinear functional boundary conditions in a unified way

2005 ◽  
Vol 63 (5-7) ◽  
pp. e2515-e2524 ◽  
Author(s):  
Alberto Cabada ◽  
José Ángel Cid
Keyword(s):  
Boundary Conditions ◽  
Extremal Solutions ◽  
Nonlinear Functional ◽  
Functional Boundary ◽  
Functional Boundary Conditions

Bounding Surfaces and Second Order Quasilinear Equations with Compatible Nonlinear Functional Boundary Conditions

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Jean Mawhin ◽  
Bevan Thompson
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Existence Results ◽  
Quasilinear Equations ◽  
Nonlinear Functional ◽  
Special Cases ◽  
Functional Boundary ◽  
Functional Boundary Conditions ◽  
Bounding Surfaces

AbstractWe establish existence results for solutions to functional boundary value problems for φ- Laplacian ordinary differential equations assuming there are lower and upper solutions and Lipschitz bounding surfaces for the derivative which we adapt to our problem. Our results apply to some problems which do not satisfy Nagumo growth bounds. Moreover they contain as special cases many results for the p- and ɸ-Laplacians as well as many results where the boundary conditions depend on n-points or even functionals. Our boundary conditions generalize those of Fabry and Habets, Cabada and Pouso, Cabada, O’Regan and Pouso, and many others.

scholarly journals EXISTENCE OF A SOLUTION FOR A SINGULAR DIFFERENTIAL EQUATION WITH NONLINEAR FUNCTIONAL BOUNDARY CONDITIONS

2007 ◽  
Vol 49 (2) ◽  
pp. 213-224 ◽  
Author(s):  
ALBERTO CABADA ◽  
JOSÉ ÁNGEL CID
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Diffusion Processes ◽  
Singular Differential Equation ◽  
Existence Of A Solution ◽  
Nonlinear Functional ◽  
Local Boundary ◽  
Functional Boundary ◽  
Non Local ◽  
Functional Boundary Conditions

AbstractIn this paper we deal with some boundary value problems related with diffusion processes in the presence of lower and upper solutions. Singularities as well as non local boundary conditions are allowed. We also prove the existence of extremal solutions and the uniqueness of solution for a particular case.

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