Remarks on nonlocal boundary value problems at resonance

2010 ◽  
Vol 216 (2) ◽  
pp. 497-500 ◽  
Author(s):  
J.R.L. Webb
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Value Problems ◽  
At Resonance

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.

Second order nonlocal boundary value problems at resonance

2011 ◽  
Vol 284 (7) ◽  
pp. 875-884 ◽  
Author(s):  
Daniel Franco ◽  
Gennaro Infante ◽  
Mirosława Zima
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Second Order ◽  
Nonlocal Boundary Value Problems ◽  
At Resonance

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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