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. <i>Electronic Journal of Differential Equations, 2016</i>(40), pp. 1-13.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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