# Boundary Value Problems

Boundary Value Problems > 2019 > 2019 > 1 > 1-17

Boundary Value Problems > 2019 > 2019 > 1 > 1-16

*x*. By using the non-Nehari...

Boundary Value Problems > 2019 > 2019 > 1 > 1-16

Boundary Value Problems > 2019 > 2019 > 1 > 1-17

In this paper, the authors investigate the existence and multiplicity of solutions for the following fractional Hamiltonian system: {D∞αt(−∞Dtαu(t))+V(t)u(t)=λu(t)+b(t)|u(t)|q−2u(t)+μh(t),t∈R,u∈Hα(R,RN), $$\textstyle\begin{cases} { }_{t}D_{\infty }^{\alpha } ( {{ }_{-\infty }D_{t}^{\alpha }u(t)} )+V(t)u(t)=\lambda u(t)+b(t) \vert u(t) \vert ^{q-2}u(t)+\mu h(t),\quad t \in \mathbb{R}, \\ u\in H^{\alpha...

Boundary Value Problems > 2019 > 2019 > 1 > 1-16

This paper is dedicated to studying the following Schrödinger–Poisson system: {−△u+V(x)u+K(x)ϕ(x)u=f(x,u),x∈R3,−△ϕ=K(x)u2,x∈R3, $$ \textstyle\begin{cases} -\triangle u+V(x)u+K(x)\phi (x)u=f(x, u), \quad x\in {\mathbb {R}}^{3}, \\ -\triangle \phi =K(x)u^{2}, \quad x\in {\mathbb {R}}^{3}, \end{cases} $$ where V(x) $V(x)$, K(x) $K(x)$, and f(x,u) $f(x, u)$ are periodic in *x*. By using the non-Nehari...

Boundary Value Problems > 2019 > 2019 > 1 > 1-16

In this paper, we study the existence of ground state solutions to the following fractional Schrödinger system with linear and nonlinear couplings: {(−△)su+(λ1+V(x))u+kv=μ1u3+βuv2,in R3,(−△)sv+(λ2+V(x))v+ku=μ2v3+βu2v,in R3,u,v∈Hs(R3), $$ \textstyle\begin{cases} (-\triangle )^{s}u+(\lambda _{1}+V(x))u+kv=\mu _{1}u^{3}+\beta uv^{2}, \quad \text{in } R^{3},\\ (-\triangle )^{s}v+(\lambda _{2}+V(x))v+ku=\mu...