Resonance and nonlinearity: A survey

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C. Fabry and J. Mawhin, “Oscillations of a forced asymmetric oscillator at resonance,” Nonlinearity, 13, 493–505 (2000).

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A. Fonda and J. Mawhin, “Planar differential systems at resonance,” Adv. Different. Equat. (to appear).

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M. Kunze, T. Kupper, and Bin Liu, “Boundedness and unboundedness of solutions of reversible oscillators at resonance,” Nonlinearity, 14, 1105–1122 (2001).

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Bin Liu, “Boundedness in asymmetric oscillations,” J. Math. Anal. Appl., 231, 355–373 (1999).

Bin Liu, “Boundedness in nonlinear oscillations at resonance,” J. Different. Equat., 153, 142–174 (1999).

Bin Liu, “Quasiperiodic solutions of semilinear Liénard equations,” Discrete Contin. Dynam. Syst., 12, 137–160 (2005).

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R. Ortega, “On Littlewood’s problem for the asymmetric oscillator,” Rend. Semin. Mat. Fis. Milano, 68, 153–164 (1998).

R. Ortega, “Boundedness in a piecewise linear oscillator and a variant of the small twist theorem,” Proc. London Math. Soc., 79, 381–413 (1999).

R. Ortega, “Twist mappings, invariant curves and periodic differential equations,” in: Nonlinear Analysis and Its Applications to Differential Equations (Lisbon, 1998), Birkhäuser, Basel (2001), pp. 85–112.

R. Ortega, “Invariant curves of mappings with averaged small twist,” Adv. Nonlin. Stud., 1, 14–39 (2001).

R. Ortega, “Periodic perturbations of an isochronous center,” Qual. Theory Dynam. Syst., 3, 83–91 (2002).

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Dingbian Qian, “Resonance phenomena for asymmetric weakly nonlinear oscillator,” Sci. China Ser. A, 45, 214–222 (2002).

Zaihong Wang, “Multiplicity of periodic solutions of Duffing equations with jumping nonlinearities,” Acta Math. Appl. Sin. Engl. Ser., 18, 513–522 (2002).

Zaihong Wang, “Existence and multiplicity of periodic solutions of the second-order differential equations with jumping nonlinearities,” Acta Math. Appl. Sin. Engl. Ser., 615–624.

Zaihong Wang, “Periodic solutions of the second order differential equations with asymmetric nonlinearities depending on the derivatives,” Discrete Contin. Dynam. Syst., 9, 751–770 (2003).

Zaihong Wang, “Irrational rotation numbers and unboundedness of solutions of the second order differential equations with asymmetric nonlinearities,” Proc. Amer. Math. Soc., 131, 523–531 (2003).

Xiaojing Yang, “Unboundedness of the large solutions of some asymmetric oscillators at resonance,” Math. Nachr., 276, 89–102 (2004).

Xiaojing Yang, “Unbounded solutions in asymmetric oscillations,” Math. Comput. Modelling, 40, 57–62 (2004).

Xiaojing Yang, “Unbounded solutions of asymmetric oscillator,” Math. Proc. Cambridge Phil. Soc., 137, 487–494 (2004).

Xiaojing Yang, “Existence of periodic solutions in nonlinear asymmetric oscillations,” Bull. London Math. Soc., 37, 566–574 (2005).

Xiaojing Yang, “Unbounded solutions of differential equations of second order,” Arch. Math. (Basel), 85, 460–469 (2005).

Xiaojing Yang, “Existence of periodic solutions of a class of planar systems,” Z. Anal. Anwend, 25, 237–248 (2006).

Xiaojing Yang, Boundedness in Asymmetric Oscillators (to appear).

Xiaomei Zhang and Dingbian Qian, “Existence of periodic solutions for second-order differential equations with asymmetric nonlinearity,” Acta Math. Sinica (Chin. Ser.), 46, 1017–1024 (2003).