Author(s)

Xinxue Zhang, Guanggang Liu^*

School of Mathematical Sciences, Liaocheng University, Liaocheng, China.

In this paper, we consider the following noncooperative elliptic systems where Ω is a bounded domain in R^N 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 (u_k,v_k) with as k → ∞. Compared with the existing literature, we do not need to assume the behavior of the nonlinearity ∇F at infinity.

Noncooperative Elliptic Systems, (PS)^* Condition, Clark’s Theorem

Zhang, X. and Liu, G. (2023) Multiplicity of Solutions for a Class of Noncooperative Elliptic Systems. Advances in Pure Mathematics, 13, 610-619. doi: 10.4236/apm.2023.139040.