Aguerrea, Maitere; Hakl, Robert \(\sigma\)-increasing positive solutions for systems of linear functional differential inequalities of non-Metzler type. (English) Zbl 1459.34184 Mediterr. J. Math. 17, No. 6, Paper No. 181, 19 p. (2020). The authors study a system of functional differential inequalities subject to a non-local linear boundary condition. It is well-known that theorems on functional-differential inequalities play a very important role in the study of the solvability of boundary value problems in both linear and non-linear cases. In Section 4, general conditions are found for the positivity and \(\sigma\)-monotonicity of solutions to the given problem. The obtained general results are applied and further refined for some particular of the given problem such as, for instance, systems of differential inequalities with deviating arguments. Reviewer: Jiří Šremr (Brno) MSC: 34K38 Functional-differential inequalities 34K10 Boundary value problems for functional-differential equations 34K06 Linear functional-differential equations Keywords:functional differential inequality; boundary value problem; positive solution PDFBibTeX XMLCite \textit{M. Aguerrea} and \textit{R. Hakl}, Mediterr. J. Math. 17, No. 6, Paper No. 181, 19 p. (2020; Zbl 1459.34184) Full Text: DOI References: [1] Afonso, SM; Rontó, A., Measure functional differential equations in the space of functions of bounded variation, Abstr. Appl. Anal. (2013) · Zbl 1296.34146 [2] Dilna, N.; Rontó, A., General conditions guaranteeing the solvability of the Cauchy problem for functional differential equations, Math. Bohem., 133, 4, 435-445 (2008) · Zbl 1199.35131 [3] Dilna, N.; Ronto, A., Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations, Math. Slovaca, 60, 3, 327-338 (2010) · Zbl 1265.34228 [4] Domoshnitsky, A.; Hakl, R.; Šremr, J., Component-wise positivity of solutions to periodic boundary problem for linear functional differential system, J. Inequal. Appl., 112, 23 (2012) · Zbl 1278.34070 [5] Hakl, R.; Kiguradze, I.; Půža, B., Upper and lower solutions of boundary value problems for functional differential equations and theorems on functional differential inequalities, Georgian Math. J., 7, 3, 489-512 (2000) · Zbl 0980.34063 [6] Hakl, R.; Vacková, J., Bounded solutions to systems of nonlinear functional differential equations, Funct. Differ. Equ., 25, 1-2, 65-89 (2018) [7] Kiguradze, I.; Šremr, J., Solvability conditions for non-local boundary value problems for two-dimensional half-linear differential systems, Nonlinear Anal., 74, 17, 6537-6552 (2011) · Zbl 1239.34022 [8] Lomtatidze, A.; Opluštil, Z.; Šremr, J., On a nonlocal boundary value problem for first order linear functional differential equations, Mem. Differ. Equ. Math. Phys., 41, 69-85 (2007) · Zbl 1215.34076 [9] Lomtatidze, A.; Opluštil, Z.; Šremr, J., Nonpositive solutions to a certain functional differential inequality, Nelīnīĭnī Koliv, 12, 4, 461-494 (2009) · Zbl 1277.34112 [10] Lomtatidze, A.; Opluštil, Z.; Šremr, J., Solvability conditions for a nonlocal boundary value problem for linear functional differential equations, Fasc. Math., 41, 81-96 (2009) · Zbl 1207.34079 [11] Opluštil, Z.; Šremr, J., On a non-local boundary value problem for linear functional differential equations, Electron. J. Qual. Theory Differ. Equ. (2009) · Zbl 1183.34105 [12] Rontó, A.; Šremr, J., Abstract differential inequalities and the Cauchy problem for infinite-dimensional linear functional differential equations, J. Inequal. Appl., 3, 235-250 (2005) · Zbl 1105.34053 [13] Rontó, A.; Šremr, J., Equivalent solutions of nonlinear equations in a topological vector space with a wedge, J. Inequal. Appl. (2007) · Zbl 1137.47047 [14] Šremr, J., A note on two-dimensional systems of linear differential inequalities with argument deviations, Miskolc Math. Notes, 7, 2, 171-187 (2006) · Zbl 1120.34325 [15] Šremr, J., On systems of linear functional differential inequalities, Georgian Math. J., 13, 3, 539-572 (2006) · Zbl 1204.34105 [16] Šremr, J., On the Cauchy type problem for systems of functional differential equations, Nonlinear Anal., 67, 12, 3240-3260 (2007) · Zbl 1130.34035 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.