Multiplicity of Solutions for a Class of Noncooperative Elliptic Systems

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.