scholarly journals Notes on generalized boundary value problems in Banach spaces. II. Infinite-dimensional extension theory

1982 ◽  
Vol 99 (2) ◽  
pp. 271-302 ◽  
Author(s):  
Richard Brown
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Boundary Value ◽  
Extension Theory ◽  
Infinite Dimensional

scholarly journals Existence of solutions for functional boundary value problems at resonance on the half-line

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bingzhi Sun ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Half Line ◽  
Projection Scheme ◽  
At Resonance ◽  
Functional Boundary

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.

Perturbation of two-point boundary value problems with eigenvalue parameter in the boundary conditions

1983 ◽  
Vol 94 (3-4) ◽  
pp. 213-219 ◽  
Author(s):  
Lawrence Turyn
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Boundary Value ◽  
Simple Eigenvalue ◽  
Point Boundary ◽  
Eigenvalue Parameter

SynopsisWe discuss smooth changes of eigenvalues under perturbation of the boundary value problems given in the title. The simple eigenvalue criterion is developed in the setting of Banach spaces, so very general perturbations of both the differential equation and the boundary conditions are allowed. Further, we need no assumptions about self-adjointness of the original or perturbed problems. The discussion is concluded with the application of the simple eigenvalue criterion to two examples.

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