This paper considers the fractional Schrödinger-Poisson system in ℝ3. We prove that the problem has m-bump solutions under some given conditions which are given in the Introduction. Moreover, the system has more and more multi-bump solutions as ϵ → 0.

In this paper, the authors investigate the following fractional Kirchhoff boundary value problem:where the parameter λ > 0 and constants a, b > 0. By applying the mountain pass theorem and the linking theorem, some existence results on the above fractional boundary value problem are obtained. It should be pointed out that the potential V may be sign-changing.

In this paper, we study the following nonlinear problem of Kirchhoff type:where the parameter λ > 0 and 4 ≤ p < 6, constants a, b > 0. By variational methods, the results of the existence of nontrivial solutions and the concentration phenomena of the solutions as λ → +∞ are obtained. It is worth pointing out that, for the case p ∈ (4, 6), the potential V is permitted to be sign-changing.

This paper is devoted to studying the following nonlinear fractional problem: $$ \textstyle\begin{cases} (-\Delta )^{s}u+u=K( \vert x \vert )u^{p},\quad u>0, x\in {\mathbb{R}}^{N}, \\ u(x)\in H^{s}({\mathbb{R}}^{N}), \end{cases} $$ { ( − Δ ) s u + u = K ( | x | ) u p , u > 0 , x ∈ R N , u ( x ) ∈ H s ( R N ) , where $N\geq 3$ N ≥ 3 , $0< s<1$ 0 < s < 1 , $1< p<\frac{N+2s}{N-2s}$ 1 < p < N + 2 s N − 2 s , $K(|x|)$ K ( | x | ) is a positive radical function. We constructed infinitely many non-radial solutions of the new type which have a more complex concentration structure for (0.1).

In this paper, we study the existence of positive multi-peak solutions to the fractional Schrödinger–Poisson system [Formula: see text] where [Formula: see text] is a small parameter, [Formula: see text] is a positive function, [Formula: see text] and [Formula: see text] Under some given conditions which are given in Sec. ??, we prove the existence of a positive solution with m-peaks and concentrating near a given local maximum point of [Formula: see text]