Amster, Pablo; Epstein, Julián; Cuéllar, Arturo Sanjuán Periodic solutions for systems of functional-differential semilinear equations at resonance. (English) Zbl 1517.34092 Topol. Methods Nonlinear Anal. 58, No. 2, 591-607 (2021). Summary: Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay of the form \(\int_0^{2\pi}u(t+s)d\lambda (s)\), where \(\lambda\) is a finite regular signed measure. Our main technique shall be the Coincidence Degree Theorem due to Mawhin. MSC: 34K13 Periodic solutions to functional-differential equations 47N20 Applications of operator theory to differential and integral equations 47H11 Degree theory for nonlinear operators Keywords:periodic solutions; functional-differential equations; Lazer-Leach conditions; coincidence degree × Cite Format Result Cite Review PDF Full Text: arXiv References: [1] P. Amster, A. Deboli and M.P. Kuna, Lazer-Leach conditions for coupled Gompertzlike delayed systems, Appl. Math. Lett. 83 (2018), 53-58. · Zbl 1489.34116 [2] P. Amster and P. De Napoli, On a generalization of Lazer-Leach conditions for a system of second order ODE’s, Topol. Methods Nonlinear Anal. 33 (2009), no. 1, 31-39. · Zbl 1189.34037 [3] X. Fu and S. Zhang, Periodic solutions for differential equations at resonance with unbounded nonlinearities, Nonlinear Anal. 52 (2003), no. 3, 755-767. · Zbl 1027.34076 [4] A.C. Lazer, On Schauder’s fixed point theorem and forced second-order nonlinear oscillations, J. Math. Anal. Appl. 21 (1968), no. 2, 421-425. · Zbl 0155.14001 [5] A.C. Lazer and D.E. Leach, Bounded perturbations of forced harmonic oscillators at resonance, Ann. Mat. Pura Appl. 82 (1969), no. 4, 49-68. · Zbl 0194.12003 [6] S. Ma, Z. Wang and J. Yu, An abstract existence theorem at resonance and its applications, J. Differential Equations 145 (1998), no. 2, 274-294. · Zbl 0940.34056 [7] J. Mawhin, Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces, J. Differential Equations 12 (1972), 610-636. · Zbl 0244.47049 [8] F.L. Nazarov, Local estimates for exponential polynomials and their applications to inequalities of the uncertainty principle type, Algebra i Analiz 5 (1993), no. 4, 3-66. · Zbl 0822.42001 [9] L. Nirenberg, Generalized degree and nonlinear problems, Contributions to Nonlinear Functional Analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971), Academic Press, New York, 1971, pp. 1-9. · Zbl 0267.47034 [10] K. Wang and S. Lu, On the existence of periodic solutions for a kind of high-order neutral functional differential equations. J. Math. Anal. Appl 326 (2007), no. 2, 1161-1173. · Zbl 1113.34054 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.