On a variational approach to some non-local boundary value problems

2005 ◽  
Vol 84 (9) ◽  
pp. 909-925 ◽  
Author(s):  
J. M. Gomes ◽  
L. Sanchez
Keyword(s):  
Boundary Value Problems ◽  
Variational Approach ◽  
Boundary Value ◽  
Local Boundary ◽  
Non Local

scholarly journals Non-trivial solutions of local and non-local Neumann boundary-value problems

2016 ◽  
Vol 146 (2) ◽  
pp. 337-369 ◽  
Author(s):  
Gennaro Infante ◽  
Paolamaria Pietramala ◽  
F. Adrián F. Tojo
Keyword(s):  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Linear Operators ◽  
Local Boundary ◽  
Hammerstein Integral Equations ◽  
Neumann Type ◽  
Non Local ◽  
Neumann Boundary Value Problems

We prove new results on the existence, non-existence, localization and multiplicity of non-trivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed-point index. Some of the criteria involve a comparison with the spectral radius of some related linear operators. We apply our results to some boundary-value problems with local and non-local boundary conditions of Neumann type. We illustrate in some examples the methodologies used.

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