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<p>Dealing with a forced system ruled by a positively-(<i>p</i>,&#xa0;<i>q</i>)-homogeneous Hamiltonian function and a friction term, we propose a nonresonance condition in order to generalize a classical result by Frederickson and Lazer. We are thus able to treat both the periodic problem and the boundedness problem. In particular, our results apply to scalar <i>p</i>-Laplacian equations with asymmetric nonlinearities.</p>

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Perturbed positively-(p, q)-homogeneous Hamiltonian systems with Frederickson–Lazer conditions

  • 期刊论文

  • 发表日期：

    2025年1月13日

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  • Alessandro Fonda,
  • Natnael Gezahegn Mamo,
  • Andrea Sfecci,
  • Wahid Ullah

摘要

Dealing with a forced system ruled by a positively-(p, q)-homogeneous Hamiltonian function and a friction term, we propose a nonresonance condition in order to generalize a classical result by Frederickson and Lazer. We are thus able to treat both the periodic problem and the boundedness problem. In particular, our results apply to scalar p-Laplacian equations with asymmetric nonlinearities.