Approximation Methods for Two-Point Boundary Value Problems with Nonlinear Boundary Conditions

1976 ◽  
Vol 13 (3) ◽  
pp. 405-411 ◽  
Author(s):  
G. W. Reddien
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Approximation Methods ◽  
Point Boundary

scholarly journals Nonlocal systems of BVPS with asymptotically sublinear boundary conditions

2012 ◽  
Vol 6 (2) ◽  
pp. 174-193 ◽  
Author(s):  
Christopher Goodrich
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Coupled System ◽  
Nonlinear Boundary Conditions ◽  
Borel Measures ◽  
Boundary Functions ◽  
Nonlocal Terms ◽  
Nonlocal Nonlinear

In this paper we consider a coupled system of second-order boundary value problems with nonlocal, nonlinear boundary conditions. By imposing only a condition of asymptotic sublinear growth on the nonlinear boundary functions, we are able to achieve generalizations over existing works and, in particular, we allow for the nonlocal terms to be able to be represented as Lebesgue-Stieltjes integrals possessing signed Borel measures. Because we only suppose the sublinearity of the nonlinear boundary functions at positive infinity, we also remove many of the restrictive growth assumptions found in other recent works on closely related problems. We conclude with a numerical example to explicate the consequences of our main result.

scholarly journals TWO INITIAL-BOUNDARY VALUE PROBLEMS WITH NONLINEAL BOUNDARY CONDITIONS FOR ONE-DIMENSION HYPERBOLIC EQUATION

2017 ◽  
Vol 17 (2) ◽  
pp. 46-56
Author(s):  
L.S. Pulkina ◽  
M.V. Strigun
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Nonlinear Boundary Conditions ◽  
One Dimension ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

In this paper, the initial-boundary value problems for hyperbolic equationwith nonlinear boundary conditions are considered. Existence and uniqueness ofgeneralized solution are proved.

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