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 Nonzero Positive Solutions of Elliptic Systems with Gradient Dependence and Functional BCs

2020 ◽  
Vol 20 (4) ◽  
pp. 911-931 ◽  
Author(s):  
Stefano Biagi ◽  
Alessandro Calamai ◽  
Gennaro Infante
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence Result ◽  
Elliptic Systems ◽  
Existence Results ◽  
Topological Methods ◽  
Elliptic Differential Equations ◽  
Nonnegative Solutions ◽  
Functional Boundary ◽  
Functional Boundary Conditions

AbstractWe discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradient terms in the nonlinearities. We prove the existence of nonnegative solutions and provide a non-existence result. We present some examples to illustrate the applicability of the existence and non-existence results.

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

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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