Consider the Kirchhoff type equation \begin{equation}\label{eq0.1}-\left(a+b\int_{\mathbb{R}^{N}}|\nabla u|^{2}\,dx\right) \Delta u=\left(\frac{1}{|x|^\mu}*F(u)\right)f(u)\ \ \mbox{in}\ \mathbb{R}^N, \ \ u\in D^{1,2}(\mathbb{R}^N), ~~~~~~(0.1)\end{equation}where $a>0$, $b\geq0$, $0<\mu<\min\{N, 4\}$ with $N\geq 3$, $f: \mathbb{R}\to\mathbb{R}$ is a continuous function and $F(u)=\int_0^u f(t)\,dt$. Under some general assumptions on $f$, we establish the existence of a nontrivial spherically symmetric solution for problem (0.1). The proof is mainly based on mountain pass approach and a scaling technique introduced by Jeanjean. 相似文献
Decontamination of aqueous heavy metal is a challenging task of environmental remediation. Herein, we demonstrated an adsorptive method for efficient removal of aqueous Hg(II) using a magnetic nanocomposite Fe3O4/graphene oxide (Fe3O4/GO). Adsorption of Hg(II) onto Fe3O4/GO equilibrated in 4 min, with the adsorption percent and quantity of 91.17% and 547.01 mg g?1, respectively. Fe3O4/GO can be easily recovered from solution via magnetic separation for reuse, and retaining 73.5% of its original capacity after five consecutive cycles. The Temkin model and PSO model were most suitable for describing adsorption in equilibrium and non-equilibrium state, respectively. Both GO and Fe3O4 adsorbed Hg(II) via donating electrons in oxygen atoms toward Hg(II). Moreover, GO made a major contribution, while Fe3O4 made a minor one to adsorption. The facile preparation, high adsorption efficiency, easy recovery, and reusability may enable Fe3O4/GO to be a promising adsorbent for aqueous Hg(II).
Research on Chemical Intermediates - Water pollution caused by heavy metals is a severe environmental issue. In this work, a graphene oxide–starch composite (GO/WS) was facilely prepared via... 相似文献