Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R 3 $\mathbb{R}^{3}$

Abstract

In this paper, we study the following Kirchhoff-Schrödinger-Poisson systems:-(a + b R 3 |∇u| 2 dx) u + V(x)u + φu = f (u), x ∈ R 3 ,-φ = u 2 , x ∈ R 3 , where a, b are positive constants, V ∈ C(R 3 , R +). By using constraint variational method and the quantitative deformation lemma, we obtain a least-energy sign-changing (or nodal) solution u b to this problem, and study the energy property of u b. Moreover, we investigate the asymptotic behavior of u b as the parameter b 0.

Ground state and nodal solutions for critical Kirchhoff–Schrödinger–Poisson systems with an asymptotically 3-linear growth nonlinearity

“…Comparing with the literature works, the above three results can be regarded as a generalization of those in [12,19,20]. As for Kirchhoff-Schrödinger-Poisson equation, to the best of our knowledge, few results involved the existence and asymptotic behavior of ground state nodal solutions in case of critical growth.…”

“…Note that, since system (1.7) involved pure critical nonlinearity |u| 4 u, it will prevent us from using the standard arguments as in [3,12,19,22]. Hence, we need to show some techniques to overcome the lack of compactness in E → L 6 (R 3 ).…”

Infinitely many high energy radial solutions for a Kirchhoff-Schrödinger-Poisson system

“…After Benci and Fortunato [2], system (1.1) has been extensively studied; see, e.g., [15,16,17,20,23,25]. In [15,23], the authors studied the existence of high energy solutions of the Kirchhoff-Schrödinger problem in the following form…”

Existence of least energy nodal solution for Kirchhoff–Schrödinger–Poisson system with potential vanishing

“…Inspired by the works mentioned, especially by [10,13,15,35,45], in this paper, we find the nodal solutions to system (1.1) under some weaker assumptions on f . As in [1], we say that (V , K) ∈ K if continuous functions V , K : R 3 → R satisfy the following conditions:…”

“…Via a gluing method, Deng and Yang [10] studied the nodal solutions for system (1.1) with f (u) = |u| p-2 u, p ∈ (4, 6). Wang, Li, and Hao [35]studied the existence and asymptotic behavior of a least energy nodal solution for system (1.1) by using the constraint variation methods.…”