Journal of Differential Equations最新文献

英文中文

Multiple solutions for quasi-linear elliptic equations with lack of symmetry 缺乏对称性的拟线性椭圆方程的多重解

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-05-05 Epub Date: 2026-02-04 DOI: 10.1016/j.jde.2026.114177

Chen Huang , Youjun Wang , Jianjun Zhang

This paper investigates the existence of multiple solutions for a class of generalized quasi-linear elliptic equations on

R^{N}

with lack of symmetry. The primary challenges in addressing such problem stem from the loss of smoothness and compactness in the associated energy functional. To overcome these obstacles, we introduce a variational perturbation method inspired by the approach developed by Liu-Liu-Wang (2019) [23]. Subsequently, by employing an abstract critical point theorem along with Moser's iteration technique, we establish the existence of arbitrarily many critical points for the corresponding non-smooth and non-even functionals.

研究了一类缺乏对称性的广义拟线性椭圆型方程的多重解的存在性。解决这类问题的主要挑战源于相关能量泛函的平滑性和紧致性的丧失。为了克服这些障碍，我们引入了一种受Liu-Liu-Wang(2019)[23]开发的方法启发的变分摄动方法。随后，利用抽象临界点定理和Moser迭代技术，建立了相应的非光滑非偶泛函的任意多临界点的存在性。

引用次数: 0

Variational construction of asymptotic orbits in contact Hamiltonian systems 接触哈密顿系统渐近轨道的变分构造

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-05-05 Epub Date: 2026-01-23 DOI: 10.1016/j.jde.2026.114141

Liang Jin , Jun Yan , Kai Zhao

For contact Hamiltonian systems without monotonicity assumption, there is a family of invariant sets

{{\tilde{N}}_{u}}

naturally stratified by the solutions u to the corresponding Hamilton-Jacobi equation. Under convergence assumptions of the solution semigroup, we establish the existence of semi-infinite orbits asymptotic to some

{\tilde{N}}_{u}

and heteroclinic orbits between

{\tilde{N}}_{u}

and

{\tilde{N}}_{v}

for different solutions u and v by variational methods. We also give verifiable criteria to ensure the convergence assumptions. As a corollary, we give a description of action minimizing orbits of the model system studied in [26].

对于无单调性假设的接触哈密顿系统，存在一类由相应哈密顿-雅可比方程解自然分层的不变集{N ~ u}。在解半群的收敛假设下，用变分方法证明了不同解u和v的半无限轨道渐近于某些N ~ u和N ~ u与N ~ v之间的异斜轨道的存在性。并给出了收敛性假设的可验证准则。作为推论，我们给出了[26]中所研究的模型系统的作用最小轨道的描述。

{"title":"Variational construction of asymptotic orbits in contact Hamiltonian systems","authors":"Liang Jin , Jun Yan , Kai Zhao","doi":"10.1016/j.jde.2026.114141","DOIUrl":"10.1016/j.jde.2026.114141","url":null,"abstract":"<div><div>For contact Hamiltonian systems without monotonicity assumption, there is a family of invariant sets <span><math><mo>{</mo><msub><mrow><mover><mrow><mi>N</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>u</mi></mrow></msub><mo>}</mo></math></span> naturally stratified by the solutions <em>u</em> to the corresponding Hamilton-Jacobi equation. Under convergence assumptions of the solution semigroup, we establish the existence of semi-infinite orbits asymptotic to some <span><math><msub><mrow><mover><mrow><mi>N</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>u</mi></mrow></msub></math></span> and heteroclinic orbits between <span><math><msub><mrow><mover><mrow><mi>N</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>u</mi></mrow></msub></math></span> and <span><math><msub><mrow><mover><mrow><mi>N</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>v</mi></mrow></msub></math></span> for different solutions <em>u</em> and <em>v</em> by variational methods. We also give verifiable criteria to ensure the convergence assumptions. As a corollary, we give a description of action minimizing orbits of the model system studied in <span><span>[26]</span></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114141"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146025659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

High multiplicity and global structure of coexistence states in a predator-prey model with saturation 饱和捕食-食饵模型中共存状态的高多样性和全局结构

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-05-05 Epub Date: 2026-01-20 DOI: 10.1016/j.jde.2026.114116

Kousuke Kuto , Julián López-Gómez , Eduardo Muñoz-Hernández

This paper establishes that, under the appropriate range of values of the parameters involved in the formulation of the model, a diffusive predator-prey system with saturation can have an arbitrarily large number of coexistence states for sufficiently large saturation rates. Moreover, it ascertains the global structure of the set of coexistence states in the limiting system as the saturation rate blows up.

本文建立了在模型公式中所涉及的参数的适当取值范围内，对于足够大的饱和率，具有饱和的扩散捕食-食饵系统可以具有任意多的共存状态。此外，还确定了饱和速率爆炸时极限系统共存状态集的全局结构。

引用次数: 0

The strongly nonlocal Allen–Cahn problem 强非局部Allen-Cahn问题

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-05-05 Epub Date: 2026-01-30 DOI: 10.1016/j.jde.2026.114168

Erisa Hasani, Stefania Patrizi

We study the sharp interface limit of the fractional Allen–Cahn equation

ε \partial_{t} u^{ε} = I_{n}^{s} [u^{ε}] - \frac{1}{ε^{2 s}} W^{'} (u^{ε}) in (0, \infty) \times R^{n}, n \geq 2,

where

ε > 0

I_{n}^{s} = - c_{n, s} {(- Δ)}^{s}

is the fractional Laplacian of order

2 s \in (0, 1)

R^{n}

, and W is a smooth double-well potential with minima at 0 and 1. We focus on the singular regime

s \in (0, \frac{1}{2})

, corresponding to strongly nonlocal diffusion. For suitably prepared initial data, we prove that the solution

u^{ε}

converges, as

ε \to 0

, to the minima of W with the interface evolving by fractional mean curvature flow. This establishes the first rigorous convergence result in this regime, complementing and completing previous work for

s \geq \frac{1}{2}

我们研究了分数阶Allen-Cahn方程ε∂tuε=Ins[uε]−1ε2sW ' (uε)in（0,∞）×Rn,n≥2，其中ε>；0, Ins=−cn,s（−Δ）s是Rn中2s阶的分数阶拉普拉斯算子∈(0,1)，W是一个在0和1处有极小值的光滑双阱势。我们关注奇异区域s∈(0,12)，对应于强非局部扩散。对于适当准备的初始数据，我们证明了当ε→0时，随着分数阶平均曲率流的界面演化，解收敛到W的最小值。这建立了该区域的第一个严格的收敛结果，补充并完成了先前关于s≥12的工作。

引用次数: 0

Existence of variational solutions to doubly nonlinear systems in general noncylindrical domains 一般非圆柱形域上双非线性系统变分解的存在性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-05-05 Epub Date: 2026-01-27 DOI: 10.1016/j.jde.2026.114139

Leah Schätzler , Christoph Scheven , Jarkko Siltakoski , Calvin Stanko

We consider the Cauchy–Dirichlet problem to doubly nonlinear systems of the form

\partial_{t} (| u |^{q - 1} u) - div (D_{ξ} f (x, u, D u)) = - D_{u} f (x, u, D u)

with

q \in (0, \infty)

in a bounded noncylindrical domain

E \subset R^{n + 1}

. Further, we suppose that

x \mapsto f (x, u, ξ)

is integrable, that

(u, ξ) \mapsto f (x, u, ξ)

is convex, and that f satisfies a p-growth and -coercivity condition for some

p > \max {1, \frac{n (q + 1)}{n + q + 1}}

. Merely assuming that

L^{n + 1} (\partial E) = 0

, we prove the existence of variational solutions

u \in L^{\infty} (0, T; L^{q + 1} (E, R^{N}))

. If E does not shrink too fast, we show that for the solution u constructed in the first step,

| u |^{q - 1} u

admits a distributional time derivative. Moreover, under suitable conditions on E and the stricter lower bound

p \geq \frac{(n + 1) (q + 1)}{n + q + 1}

, u is continuous with respect to time.

我们考虑在有界非柱面区域E∧Rn+1中，∂t(|u|q−1u)−div(Dξf(x,u,Du))=−Duf（x,u,Du）的双非线性系统的Cauchy-Dirichlet问题。进一步，我们假设x∑f（x,u,ξ）是可积的，(u,ξ)∑f（x,u,ξ）是凸的，并且f对于某些p>；max (1,n(q+1)n+q+1}满足p增长和-矫顽性条件。仅假设Ln+1(∂E)=0，我们证明了变分解u∈L∞（0，T;Lq+1(E，RN)）的存在性。如果E收缩得不是太快，我们证明了对于第一步构造的解u， |u|q−1u允许一个分配时间导数。并且，在E的适当条件下，以及p≥(n+1)(q+1)n+q+1的更严格下界下，u相对于时间是连续的。

引用次数: 0

Acceleration or finite speed propagation in integro-differential equations with logarithmic Allee effects 具有对数Allee效应的积分-微分方程中的加速或有限速度传播

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-05-05 Epub Date: 2026-01-28 DOI: 10.1016/j.jde.2026.114136

Émeric Bouin , Jérôme Coville , Xi Zhang

This paper is devoted to studying propagation phenomena in integro-differential equations with a weakly degenerate non-linearity. The reaction term can be seen as an intermediate between the classical logistic (or Fisher-KPP) non-linearity and the standard weak Allee effect one. We study the effect of the tails of the dispersal kernel on the rate of expansion. When the tail of the kernel is sub-exponential, the exact separation between existence and non-existence of travelling waves is exhibited. This, in turn, provides the exact separation between finite speed propagation and acceleration in the Cauchy problem. Moreover, the exact rates of acceleration for dispersal kernels with sub-exponential and algebraic tails are provided. Our approach is generic and covers a large variety of dispersal kernels including those leading to convolution and fractional Laplace operators. Numerical simulations are provided to illustrate our results.

研究一类弱退化非线性积分-微分方程的传播现象。反应项可以看作是经典logistic（或Fisher-KPP）非线性和标准弱Allee效应非线性之间的中间项。我们研究了扩散核尾部对膨胀速率的影响。当核的尾部为次指数时，行波的存在与不存在表现出精确的分离。这反过来又提供了柯西问题中有限速度传播和加速度之间的精确分离。此外，还给出了具有次指数尾和代数尾的扩散核的精确加速率。我们的方法是通用的，涵盖了大量的分散核，包括那些导致卷积和分数拉普拉斯算子。数值模拟说明了我们的结果。

引用次数: 0

Quantitative blow-up via renormalized Kato theory: Resolving Nakao-type systems 通过重整加藤理论的定量爆炸：解决中尾型系统

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-05-05 Epub Date: 2026-01-29 DOI: 10.1016/j.jde.2026.114165

Mengyun Liu

We address the fundamental obstruction identified in [10, Remark 3] for system (1) where sign-changing kernels when

b^{2} < 4 k

preclude blow-up arguments via nonnegative functionals—by partially resolving it in the regime

b^{2} < k

Building upon Kato-type techniques, we develop a renormalized iteration scheme establishing the quantitative upper bounds for blow-up times. This framework resolves the critical case

b^{2} < k

for

b, k > 0

under

θ (p, q, n) : = \frac{1}{p q - 1} - \frac{n - 1}{2} \geq 0

. When combined with [10]'s results for

b^{2} \geq 4 k

, it completes the blow-up theory for the subregime

b^{2} < k

. For

b, k < 0

, we prove blow-up in the extended critical region

Γ_{_{G G}} (p, q, n) : = \max {\frac{p + 1}{p q - 1}, \frac{q + 1}{p q - 1}} - \frac{n - 1}{2} \geq 0,

strictly containing the classical critical set.

我们解决了在系统(1)中[10，Remark 3]中发现的基本障碍，其中当b2<；4k时的符号变化核通过非负泛函排除了爆炸参数-通过在b2<；k中部分解决了它。在加藤型技术的基础上，我们开发了一种重归一化的迭代方案，建立了爆炸时间的定量上界。该框架解决了在θ(p,q,n) =1pq−1−n−12≥0的情况下，b,k, b2<；k的临界情况。结合[10]在b2≥4k时的结果，完成了子区b2<；k的爆破理论。对于b，k<0，证明了扩展临界regionΓGG（p,q,n）的爆破性：=max (p +1pq−1,q+1pq−1}−n−12≥0，严格包含经典临界集。

引用次数: 0

On the well-posedness of (nonlinear) rough continuity equations （非线性）粗糙连续方程的适定性

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-05-05 Epub Date: 2026-01-20 DOI: 10.1016/j.jde.2026.114124

Lucio Galeati , James-Michael Leahy , Torstein Nilssen

Motivated by applications to fluid dynamics, we study rough differential equations (RDEs) and rough partial differential equations (RPDEs) with non-Lipschitz drifts. We prove well-posedness and existence of a flow for RDEs with Osgood drifts, as well as well-posedness of weak

L^{p}

-valued solutions to linear rough continuity and transport equations on

R^{d}

under DiPerna–Lions regularity conditions; a combination of the two then yields flow representation formulas for linear RPDEs. We apply these results to obtain existence, uniqueness and continuous dependence for

L^{1} \cap L^{\infty}

-valued solutions to a general class of nonlinear continuity equations. In particular, our framework covers the 2D Euler equations in vorticity form with rough transport noise, providing a rough analogue of Yudovich's theorem. As a consequence, we construct an associated continuous random dynamical system, when the driving noise is a fractional Brownian motion with Hurst parameter

H \in (1 / 3, 1)

. We further prove weak existence of solutions for initial vorticities in

L^{1} \cap L^{p}

, for any

p \in [1, \infty)

受流体力学应用的启发，我们研究了具有非lipschitz漂移的粗糙微分方程和粗糙偏微分方程。证明了具有Osgood漂移的RDEs的流的适定性和存在性，以及在DiPerna-Lions正则性条件下线性粗糙连续性和输运方程的弱lp值解的适定性；两者的结合就产生了线性rpde的流表示公式。应用这些结果得到了一类非线性连续方程L1∩L∞值解的存在唯一性和连续相依性。特别地，我们的框架涵盖了具有粗糙输运噪声的涡度形式的二维欧拉方程，提供了对Yudovich定理的粗略模拟。因此，我们构造了一个关联的连续随机动力系统，当驱动噪声为分数阶布朗运动，Hurst参数H∈(1/3,1)。我们进一步证明了对于任意p∈[1，∞]，L1∩Lp中初始涡度解的弱存在性。

{"title":"On the well-posedness of (nonlinear) rough continuity equations","authors":"Lucio Galeati , James-Michael Leahy , Torstein Nilssen","doi":"10.1016/j.jde.2026.114124","DOIUrl":"10.1016/j.jde.2026.114124","url":null,"abstract":"<div><div>Motivated by applications to fluid dynamics, we study rough differential equations (RDEs) and rough partial differential equations (RPDEs) with non-Lipschitz drifts. We prove well-posedness and existence of a flow for RDEs with Osgood drifts, as well as well-posedness of weak <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-valued solutions to linear rough continuity and transport equations on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> under DiPerna–Lions regularity conditions; a combination of the two then yields flow representation formulas for linear RPDEs. We apply these results to obtain existence, uniqueness and continuous dependence for <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-valued solutions to a general class of nonlinear continuity equations. In particular, our framework covers the 2D Euler equations in vorticity form with rough transport noise, providing a rough analogue of Yudovich's theorem. As a consequence, we construct an associated continuous random dynamical system, when the driving noise is a fractional Brownian motion with Hurst parameter <span><math><mi>H</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>/</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. We further prove weak existence of solutions for initial vorticities in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>, for any <span><math><mi>p</mi><mo>∈</mo><mo>[</mo><mn>1</mn><mo>,</mo><mo>∞</mo><mo>)</mo></math></span>.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"462 ","pages":"Article 114124"},"PeriodicalIF":2.3,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146001826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stability and asymptotic behavior of one-dimensional solutions in cylinders 柱体一维解的稳定性和渐近性质

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-05-05 Epub Date: 2026-01-28 DOI: 10.1016/j.jde.2026.114146

Francesca De Marchis, Lisa Mazzuoli, Filomena Pacella

We consider positive one-dimensional solutions of a Lane-Emden relative Dirichlet problem in a cylinder and study their stability/instability properties as the energy varies with respect to domain perturbations. This depends on the exponent

p > 1

of the nonlinearity and we obtain results for p close to 1 and for p large. This is achieved by a careful asymptotic analysis of the one-dimensional solution as

p \to 1

p \to \infty

, which is of independent interest. It allows to detect the limit profile and other qualitative properties of these solutions.

考虑圆柱中Lane-Emden相对狄利克雷问题的一维正解，研究了它们在能量随域扰动变化时的稳定性和不稳定性。这取决于非线性的指数p>；1我们得到了p接近1和p较大时的结果。这是通过对p→1或p→∞的一维解进行仔细的渐近分析来实现的，这是一个独立的兴趣。它允许检测这些溶液的极限轮廓和其他定性性质。

引用次数: 0

Dynamics of an on-off self-propelled particle in a cellular flow 细胞流动中开-关自推进粒子的动力学

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2026-05-05 Epub Date: 2026-01-26 DOI: 10.1016/j.jde.2026.114127

Alfredo J. Grados, Jeferson Cassiano, Maurício F.S. Lima, Rafael D. Vilela

On-off swimming mechanisms are common in natural and artificial microswimmers. A mathematically sound modeling of the dynamics of particles exhibiting such mechanisms should be based on discontinuous vector fields. Nevertheless, the relatively new techniques constructed to deal with discontinuous systems have not been employed for microswimmers. Here, motivated by the “run” strategy proposed in T. Mano et al. (2017) [11] for motile Janus particles, we study the dynamics of swimmers with self-propulsion when their orientation is close to a given direction. Unlike the dynamics addressed in the aforementioned reference, we consider that swimmers are immersed in a fluid flow. Their orientation, therefore, evolves according to Jeffery's equation. We use the Filippov formalism for discontinuous systems to geometrically describe the velocity field. We also derive a Poincaré map, which describes the dynamics to first order in the discontinuity parameter, and study some of its properties.

开关游泳机制在天然和人工微游泳者中很常见。表现出这种机制的粒子动力学的数学上合理的建模应该基于不连续的矢量场。然而，为处理不连续系统而构建的相对较新的技术尚未用于微游泳者。在T. Mano et al.(2017)[11]中针对运动Janus粒子提出的“奔跑”策略的激励下，我们研究了具有自我推进的游泳者在其方向接近给定方向时的动力学。与前面提到的动力学不同，我们认为游泳者沉浸在流体流动中。因此，它们的方向根据杰弗瑞的方程演变。我们用不连续系统的菲利波夫形式来几何地描述速度场。我们还得到了一个在不连续参数上描述动力学到一阶的庞卡罗映射，并研究了它的一些性质。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Differential Equations

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀