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

Infinitely many solutions for a gauged nonlinear Schrödinger equation with a perturbation

In this paper, we use the Fountain theorem under the Cerami condition to study the gauged nonlinear Schrödinger equation with a perturbation in R2. Under some appropriate conditions, we obtain the existence of infinitely many high energy solutions for the equation

Book of Abstracts

USPCAPESFAPESPCNPqINCTMatICMC Summer Meeting on Differentail Equations.\ud São Carlos, Brasil. 3-7 february 2014