A vector p-Laplacian type approach to multiple periodic solutions for the p-relativistic operator

作者：Jebelean Petru^*; Mawhin Jean; Serban Calin

来源：Communications in Contemporary Mathematics, 2017, 19(3): 1650029.

DOI：10.1142/S0219199716500292

• Differential inclusions
• vector p-Laplacian operator
• p-relativistic operator
• periodic solutions
• nonsmooth critical point theory
• critical orbit

We prove the existence of at least N + 1 geometrically distinct T-periodic solutions for a differential inclusions system of the form
-(Psi(u'))' epsilon partial derivative F(t, u) + h(t).
Here,Psi : R-N -> R-N is a monotone homeomorphism, F : [0, T] x R-N -> R is periodic with respect to each component of the second variable and. F(t, x) stands for the generalized Clarke gradient of F(t, center dot) at x epsilon R-N. The monotonicity assumptions on Psi highlight the vector p-Laplacian as being the prototype differential operator. The main interesting feature of this approach is that it also provides a useful framework to treat the case of the p-relativistic singular operator.

• 出版日期2017-6