σ -increasing positive solutions for systems of linear functional differential inequalities of non-Metzler type

0534004 - MÚ 2021 RIV CH eng J - Journal Article
Aguerrea, M. - Hakl, Robert
σ -increasing positive solutions for systems of linear functional differential inequalities of non-Metzler type.
Mediterranean Journal of Mathematics. Roč. 17, č. 6 (2020), č. článku 181. ISSN 1660-5446. E-ISSN 1660-5454
Institutional support: RVO:67985840
Keywords : boundary value problem * functional differential inequality
OECD category: Applied mathematics
Impact factor: 1.400, year: 2020
Method of publishing: Limited access
https://doi.org/10.1007/s00009-020-01639-8

Consider the system of functional differential inequalities: D(σ)[u'(t)-ℓ(u)(t)]≥0fora.e.t∈[a,b],φ(u)≥0,where ℓ: C([a, b] : Rn) → L([a, b] : Rn) is a linear bounded operator, φ: C([a, b] : Rn) → Rn is a linear bounded functional, σ=(σi)i=1n, where σi∈ { - 1 , 1 } , and D(σ) = diag (σ1, ⋯ , σn). In the present paper, we establish conditions guaranteeing that every absolutely continuous vector-valued function u satisfying the above-mentioned inequalities admits also the inequalities u(t) ≥ 0 for t∈ [a, b] and D(σ) u'(t) ≥ 0 for a. e. t∈ [a, b].
Permanent Link: http://hdl.handle.net/11104/0312226