scholarly journals Existence of solutions for a Boussinesq system on the half line and on a finite interval

2011 ◽  
Vol 29 (1) ◽  
pp. 25-49 ◽  
Author(s):  
Karine Adamy ◽  
Keyword(s):  
Existence Of Solutions ◽  
Finite Interval ◽  
Boussinesq System ◽  
Half Line

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.

scholarly journals The linearized classical Boussinesq system on the half‐line

2021 ◽  
Vol 146 (3) ◽  
pp. 635-657
Author(s):  
C. M. Johnston ◽  
Clarence T. Gartman ◽  
Dionyssios Mantzavinos
Keyword(s):  
Boussinesq System ◽  
Half Line

scholarly journals Higher Order Nonlocal Boundary Value Problems at Resonance on the Half-line

2020 ◽  
Vol 13 (1) ◽  
pp. 33-47
Author(s):  
Samuel Iyase ◽  
Abiodun Opanuga
Keyword(s):  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Higher Order ◽  
Half Line ◽  
Index Zero ◽  
Nonlocal Boundary Value Problems ◽  
At Resonance ◽  
Fredholm Map

This paper investigates the solvability of a class of higher order nonlocal boundaryvalue problems of the formu(n)(t) = g(t, u(t), u0(t)· · · u(n−1)(t)), a.e. t ∈ (0, ∞)subject to the boundary conditionsu(n−1)(0) = (n − 1)!ξn−1u(ξ), u(i)(0) = 0, i = 1, 2, . . . , n − 2,u(n−1)(∞) = Z ξ0u(n−1)(s)dA(s)where ξ > 0, g : [0, ∞) × <n −→ < is a Caratheodory’s function,A : [0, ξ] −→ [0, 1) is a non-decreasing function with A(0) = 0, A(ξ) = 1. The differential operatoris a Fredholm map of index zero and non-invertible. We shall employ coicidence degree argumentsand construct suitable operators to establish existence of solutions for the above higher ordernonlocal boundary value problems at resonance.

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