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

Abstract

This paper deals with the following Kirchhoff-Schrödinger-Poisson system:-(a + b R 3 |∇u| 2 dx) u + V(x)u + φu = K(x)f (u) in R 3 ,-φ = u 2 in R 3 , where a, b are positive constants, K(x), V(x) are positive continuous functions vanishing at infinity, and f (u) is a continuous function. Using the Nehari manifold and variational methods, we prove that this problem has a least energy nodal solution. Furthermore, if f is an odd function, then we obtain that the equation has infinitely many nontrivial solutions.

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…”

“…Liu and He [16] obtained similar result in R 3 . By using constraint variational methods and the quantitative deformation lemma, Zhang and Wang [25] obtained a least-energy sign-changing (or nodal) solution to this problem. Using the Nehari manifold and variational methods, Wang et al [20] proved that this problem had a least energy nodal solution.…”

The Existence of Least Energy Sign-Changing Solution for Kirchhoff-Type Problem with Potential Vanishing at Infinity

“…Readers can refer to [26][27][28][29][30][31][32]. These results are also helpful for us to study (1), since (1) and ( 16) have a great correlation.…”