Existence Theorems for Nonlinear Boundary Value Problems

1974 ◽  
Vol 26 (4) ◽  
pp. 884-892 ◽  
Author(s):  
W. L. McCandless
Keyword(s):  
Nonlinear Boundary ◽  
Existence Theorems ◽  
Boundary Value ◽  
Continuous Functions ◽  
Order System ◽  
Nonlinear Boundary Value Problems ◽  
First Order ◽  
Differentiable Functions ◽  
Image Position ◽  
General Boundary Value Problem

Let C(I) denote the linear space of continuous functions from the compact interval I = [a, b] into n-dimensional real arithmetic space Rn, and let C′(I) be the subspace of continuously differentiable functions on I. A general boundary value problem for a first-order system of n ordinary differential equations on I is given by

scholarly journals Nonlinear boundary value problems for elliptic systems

1987 ◽  
Vol 30 (2) ◽  
pp. 257-272 ◽  
Author(s):  
A. Cañada
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Dimensional Space ◽  
Boundary Value ◽  
Elliptic Systems ◽  
First Eigenvalue ◽  
Nonlinear Boundary Value Problems ◽  
One Dimensional ◽  
Negative Function ◽  
Image Position

The purpose of this paper is to discuss non-linear boundary value problems for elliptic systems of the typewhere Ak is a second order uniformly elliptic operator and is such that the problemhas a one-dimensional space of solutions that is generated by a non-negative function. The boundary ∂G is supposed to be smooth and the functions gk, 1≦k≦m are defined on Ḡ×Rm and are continuously differentiate (usually, Bk represents Dirichlet or Neumann conditions and is the first eigenvalue associated with Ak and such boundary conditions).

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