Multiple periodic solutions of ordinary differential equations with bounded nonlinearities and phi-Laplacian

Bereanu, Cristian;Mawhin, Jean
(2008) No D E A - Nonlinear Differential Equations and Applications — Vol. 15, n° 1-2, p. 159-168 (2008)

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Authors
  • Bereanu, CristianUCLouvain
    Author
  • Mawhin, JeanUCLouvain
    Author
Abstract
The existence, non-existence and multiplicity of solutions to periodic boundary value problems (phi(u'))' + g(u) = e(t) + s, u(0) - u(T) = 0 = u'(0) - u'(T), is discussed, where phi : (-a, a) -> R or phi : R -> (-a, a) is an increasing homeomorphism such that phi(0) = 0 and 0 < a <= infinity. The nonlinear term g is assumed to be bounded, positive and g(+/-infinity) = 0.
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Bereanu, C., & Mawhin, J. (2008). Multiple periodic solutions of ordinary differential equations with bounded nonlinearities and phi-Laplacian. No D E A - Nonlinear Differential Equations and Applications, 15(1-2), 159-168. https://doi.org/10.1007/s00030-007-7004-x (Original work published 2008)