A vector p-Laplacian type approach to multiple periodic solutions for the p-relativistic operator
(2017) Communications in Contemporary Mathematics — Vol. 19, n° 03, p. 1650029 (2017)
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- Abstract
- We prove the existence of at least N + 1 geometrically distinct T-periodic solutions for a differential inclusions system of the form-(ψ(u′))′ ∈ ∂F(t,u) + h(t). Here, ψ: ℝN → ℝN is a monotone homeomorphism, F: [0,T] × ℝN → 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,·) at x ∈ ℝN. The monotonicity assumptions on 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.
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Jebelean, P., Mawhin, J., & Şerban, C. (2017). A vector p-Laplacian type approach to multiple periodic solutions for the p-relativistic operator. Communications in Contemporary Mathematics, 19(03), 1650029. https://doi.org/10.1142/s0219199716500292 (Original work published 2017)