TITLE:
Multiplicity of Solutions for a Class of Noncooperative Elliptic Systems
AUTHORS:
Xinxue Zhang, Guanggang Liu
KEYWORDS:
Noncooperative Elliptic Systems, (PS)* Condition, Clark’s Theorem
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.13 No.9,
September
22,
2023
ABSTRACT: In this paper, we consider the following noncooperative elliptic systems where Ω is a bounded domain in RN with smooth boundary ∂Ω, λ,δ,γ are real parameters, and . We assume that F is subquadratic at zero with respect to the variables u,v. By using a variant Clark’s theorem, we obtain infinitely many nontrivial solutions (uk,vk) with as k → ∞. Compared with the existing literature, we do not need to assume the behavior of the nonlinearity∇F at infinity.