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Application of the subharmonic Melnikov method to piecewise-smooth systems

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  • We extend a refined version of the subharmonic Melnikov method to piecewise-smooth systems and demonstrate the theory for bi- and trilinear oscillators. Fundamental results for approximating solutions of piecewise-smooth systems by those of smooth systems are given and used to obtain the main result. Special attention is paid to degenerate resonance behavior, and analytical results are illustrated by numerical ones.
    Mathematics Subject Classification: Primary: 37G15; Secondary: 34A36, 34E10.


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