Periodic solutions for systems of functional-differential semilinear equations at resonance
DOI:
https://doi.org/10.12775/TMNA.2020.078Keywords
Periodic solutions, functional-differential equations, Lazer-Leach conditions, coincidence degreeAbstract
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.References
P. Amster, A. Déboli and M.P. Kuna, Lazer–Leach conditions for coupled Gompertzlike de-layed systems, Appl. Math. Lett. 83 (2018), 53–58.
P. Amster and P. De Nápoli, 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.
X. Fu and S. Zhang, Periodic solutions for differential equations at resonance with unbounded nonlinearities, Nonlinear Anal. 52 (2003), no. 3, 755–767.
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.
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.
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.
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.
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.
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.
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.
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Copyright (c) 2021 Pablo Amster, Julián Epstein, Arturo Sanjuán Cuéllar
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
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