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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