Open AccessHigher Order Nonlocal Boundary Value Problems at Resonance on the Half-line
Author(s) -
S.A . Iyase,
A. A. Opanuga
Publication year - 2020
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v1i1.3539
Subject(s) - mathematics , invertible matrix , order (exchange) , boundary value problem , degree (music) , function (biology) , fredholm operator , mathematical analysis , boundary (topology) , resonance (particle physics) , zero (linguistics) , class (philosophy) , line (geometry) , boundary values , pure mathematics , combinatorics , geometry , physics , quantum mechanics , compact operator , philosophy , artificial intelligence , linguistics , computer science , acoustics , biology , evolutionary biology , programming language , finance , economics , extension (predicate logic)
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.