Existence and multiplicity of solutions for a class of damped-like fractional differential system - Jie Xie; Xingyong Zhang; Cuiling Liu; Danyang Kang (AIMS Mathematics, 2020)
In this paper, we obtain some results about the existence and multiplicity of weak solutions for a class of damped-like fractional differential system with a parameter $λ$. When the nonlinear term is subquadratic only near the origin, we obtain that system has a ground state weak solution $u_λ$ if $λ$ is in some given interval, and when the nonlinear term is also even near the origin, then for each $λ>0$, system has infinitely many weak solutions $\{u_n^λ\}$ with $\|u_n^λ\|→ 0$ as $n→ ∞$. We mainly use Ekeland's variational principle and a variant of Clark's theorem together with a cut-off technique to prove our results.