Problems at resonance for equations with periodic nonlinearities

Bonheure, Denis;Fabry, Christian;Ruiz, Diego
(2003) Nonlinear Analysis: Theory, Methods & Applications —

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  • Bonheure, DenisUCLouvain
    Author
  • Fabry, ChristianUCLouvain
    Author
  • Ruiz, DiegoUCLouvain
    Author
Abstract
We study differential equations with periodic nonlinearities. In particular, we prove that for a small, the equation -u" - u + g(u) = h(t) + a sin(t - phi), where g is a C-1 periodic function with zero mean value and h is orthogonal to cos t and sin t, has 2pi-periodic solutions. The proof relies on an abstract result based on variational arguments; its application makes use of integral estimates by the stationary phase method. We also study the existence of multiple solutions. (C) 2003 Elsevier Ltd. All rights reserved.
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Bonheure, D., Fabry, C., & Ruiz, D. (2003). Problems at resonance for equations with periodic nonlinearities. Nonlinear Analysis: Theory, Methods & Applications. https://doi.org/10.1016/j.na.2003.07.005