Multiple Solutions for a Class of Generalized Critical Noncooperative Schrödinger Systems in $$\mathbb {R}^N$$

Generalized noncooperative Schrödinger–Kirchhoff–type systems in RN$\mathbb {R}^N$

“…Our objective in this paper is to study the existence and multiplicity of solutions for a class of the generalized noncooperative Schrödinger-Kirchhoff-type systems with critical nonlinearity involving a general variable exponent elliptic operator in ℝ 𝑁 . More precisely, our main results of this work extend, complement, and complete several works, in particular Chems Eddine [12], Fang and Zhang [22], Huang and Li [28], Li [33], Liang and Zhang [36], and some papers listed therein.…”

“…Some similar results for the noncooperative 𝑝(𝑥)-Laplacian elliptic problems were obtained by Liang et al [35,36]. Recently, Chems Eddine [12] extended these results to the problem (1.1) when 𝐾 ≡ 1, λ is a real number, and the functions 𝑝 and 𝑞 are Lipschitz continuous. Our objective in this paper is to study the existence and multiplicity of solutions for a class of the generalized noncooperative Schrödinger-Kirchhoff-type systems with critical nonlinearity involving a general variable exponent elliptic operator in ℝ 𝑁 .…”

The Dirichlet Problem for a Class of Anisotropic Schrödinger-Kirchhoff-Type Equations With Critical Exponent

“…, N }. For further study of problems with critical exponents, we refer the reader to [2,3,4,6,7,8,10,14,15,16,17], and the references therein.…”

Multiplicity of Solutions for the Noncooperative Kirchhoff-Type Variable Exponent Elliptic System with Nonlinear Boundary Conditions

“…The novelty of this paper is as follows: in all the aforementioned papers, limit index theory [16] was applied, but the (PS) * c condition, which is described in Definition 2, should be considered. However, in the papers of Chung [15,20], Chems Eddine [21], Liang and Shi [17], Liang and Zhang [14,18,19], Li and Song [22], Sun and Bai et al [23], and Song and Shi [24], with the concentration-compactness principle [25], the boundness of the (PS)…”