Uniqueness of periodic solutions of a second order ODE implied by jump discontinuities of the coefficients. Arino, O. & Ben M'Barek, A. In Recent trends in differential equations, pages 31–45. World Sci. Publishing, River Edge, NJ, 1992.
abstract   bibtex   
We consider the following class of equations: $$d\sp 2 y\over dt\sp 2+ H\Biggl(y, dy\over dt\Biggr) y= g(y),\tag1$$ where $q$ is smooth and $H(u, v)$ is a positive constant on each of the four quadrants determined by the $u$ and $v$ axes. We prove that under conditions involving values of $H$ and the function $g$, equation (1) has one and only one nontrivial periodic solution.
@InCollection{ArinoBenMBarek1992,
  author     = {Arino, Ovide and Ben M'Barek, A.},
  title      = {Uniqueness of periodic solutions of a second order {O}{D}{E} implied by jump discontinuities of the coefficients},
  booktitle  = {Recent trends in differential equations},
  publisher  = {World Sci. Publishing},
  year       = {1992},
  pages      = {31--45},
  address    = {River Edge, NJ},
  abstract   = {We consider the following class of equations:
                  $${d\sp 2 y\over dt\sp 2}+ H\Biggl(y, {dy\over
                  dt}\Biggr) y= g(y),\tag1$$ where $q$ is smooth and
                  $H(u, v)$ is a positive constant on each of the four
                  quadrants determined by the $u$ and $v$ axes. We
                  prove that under conditions involving values of $H$
                  and the function $g$, equation (1) has one and only
                  one nontrivial periodic solution.},
  classmath  = {*34C25 Periodic solutions of ODE },
  keywords   = {jump discontinuities; periodic solution},
  mrclass    = {34C25 (34A34)},
  mrnumber   = {93i:34072},
  mrreviewer = {M. Cecchi},
}

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