Existence of solutions to fractional Hamiltonian systems with combined nonlinearities
Date
2016-01-27
Authors
Zhang, Ziheng
Yuan, Rong
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the existence of solutions for the fractional Hamiltonian system
-tDα∞(-∞Dtαu(t)) - L(t)u(t) + ∇W(t, u(t)) = 0,
u ∈ Hα(ℝ, Rn),
where α ∈ (1/2, 1), L ∈ C(ℝ, ℝn2) is a symmetric and positive definite matrix. The novelty of this article is that if τ1|u|2 ≤ (L(t)u, u) ≤ τ2|u|2 and the non-linearity W(t, u) involves a combination of superquadratic and subquadratic terms, the Hamiltonian system possesses at least two nontrivial solutions.
Description
Keywords
Fractional Hamiltonian systems, Critical point, Variational methods, Mountain pass theorem
Citation
Zhang, Z., & Yuan, R. (2016). Existence of solutions to fractional Hamiltonian systems with combined nonlinearities. Electronic Journal of Differential Equations, 2016(40), pp. 1-13.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.