Nonlocal two-point boundary-value problems in a layer with differential operators in the boundary condition

1995 ◽  
Vol 47 (8) ◽  
pp. 1283-1289 ◽  
Author(s):  
L. V. Fardigola
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Differential Operators ◽  
Boundary Value ◽  
Point Boundary

Solutions of second order multi-point boundary value problems

2008 ◽  
Vol 145 (2) ◽  
pp. 489-510 ◽  
Author(s):  
JOHN R. GRAEF ◽  
LINGJU KONG
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Nontrivial Solutions ◽  
Point Index ◽  
Linear Integral ◽  
The Relationship

AbstractWe consider classes of second order boundary value problems with a nonlinearity f(t, x) in the equations and subject to a multi-point boundary condition. Criteria are established for the existence of nontrivial solutions, positive solutions, and negative solutions of the problems under consideration. The symmetry of solutions is also studied. Conditions are determined by the relationship between the behavior of the quotient f(t, x)/x for x near 0 and ∞ and the largest positive eigenvalue of a related linear integral operator. Our analysis mainly relies on the topological degree and fixed point index theories.

scholarly journals On the Solvability of Discrete Nonlinear Two-Point Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Blaise Kone ◽  
Stanislas Ouaro
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Wirtinger Inequality

We prove the existence and uniqueness of solutions for a family of discrete boundary value problems by using discrete's Wirtinger inequality. The boundary condition is a combination of Dirichlet and Neumann boundary conditions.

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