Sign-changing solutions for a Schrödinger-Kirchhoff-Poisson system with 4-sublinear growth nonlinearity

In this paper we consider the following Schrödinger–Kirchhoff–Poisson-type system where Ω is a bounded smooth domain of R3 , a > 0, b ≥ 0 are constants and λ is a positive parameter. Under suitable conditions on Q(x) and combining the method of invariant sets of descending flow, we establish the existence and multiplicity of signchanging solutions to this problem for the case that 2 < p < 4 as λ sufficiently small. Furthermore, for λ = 1 and the above assumptions on Q(x), we obtain the same conclusions with 2 < p < 12 5

A guide to the Choquard equation

We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations $$-\Delta u + V(x)u = \bigl(|x|^{-(N-\alpha)} * |u|^p\bigr)|u|^{p - 2} u \qquad \text{in $\mathbb{R}^N$},$$ and some of its variants and extensions.Comment: 39 page