非线性分析进展 (ANONA) 旨在发表针对来自不同领域的非线性问题的选定研究贡献，特别是那些引入能够解决广泛问题的新技术的研究贡献。该杂志专注于解决纯非线性分析和应用非线性分析中的重大问题的论文。 ANONA 力求向广大读者展示该领域最重要的进展，包括数学、物理和工程领域的研究人员和研究生。

Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions addressing nonlinear problems from various fields, particularly those that introduce new techniques to solve a wide range of issues. The journal focuses on significant papers that tackle major problems in both pure and applied nonlinear analysis. ANONA strives to showcase the most important advancements in the field to a broad audience, including researchers and graduate students in mathematics, physics, and engineering.

《Advances in Nonlinear Analysis》（非线性分析进展）旨在发表来自不同领域的非线性问题的精选研究成果，特别是那些引入新技术以解决广泛问题的研究。该杂志专注于解决纯非线性分析和应用非线性分析中的重大问题，力求向广大读者展示该领域的重要进展，涵盖数学、物理和工程等领域的研究人员和研究生。

Advances in Nonlinear Analysis

Abstract This work focuses on the Kirchhoff-Schrödinger-Poisson-type system with singular term and critical Sobolev nonlinearity as follows: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:mfenced open="{" close=""> <m:mrow> <m:mtable displaystyle="true"> <m:mtr> <m:mtd columnalign="left"> <m:mo>−</m:mo> <m:mfenced open="(" close=")"> <m:mrow> <m:mi>a</m:mi> <m:mo>+</m:mo> <m:mi>b</m:mi> <m:munder> <m:mrow> <m:mrow> <m:mstyle displaystyle="true"> <m:mo>∫</m:mo> </m:mstyle> </m:mrow> </m:mrow> <m:mrow> <m:mi mathvariant="normal">Ω</m:mi> </m:mrow> </m:munder> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mrow> <m:mo>∇</m:mo> </m:mrow> <m:mi>u</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mi>p</m:mi> </m:mrow> </m:msup> <m:mi mathvariant="normal">d</m:mi> <m:mi>x</m:mi> </m:mrow> </m:mfenced> <m:msub> <m:mrow> <m:mi>Δ</m:mi> </m:mrow> <m:mrow> <m:mi>p</m:mi> </m:mrow> </m:msub> <m:mi>u</m:mi> <m:mo>+</m:mo> <m:mi>ϕ</m:mi> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mi>u</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mi>q</m:mi> <m:mo>−</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mi>λ</m:mi> <m:msup> <m:mrow> <m:mi>u</m:mi> </m:mrow> <m:mrow> <m:mo>−</m:mo> <m:mi>γ</m:mi> </m:mrow> </m:msup> <m:mo>+</m:mo> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mi>u</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:msup> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mo>∗</m:mo> </m:mrow> </m:msup> <m:mo>−</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mi>u</m:mi> <m:mspace width="1.0em"/> </m:mtd> <m:mtd columnalign="left"> <m:mstyle> <m:mspace width="0.1em"/> <m:mtext>in</m:mtext> <m:mspace width="0.1em"/> </m:mstyle> <m:mspace width="0.33em"/> <m:mi mathvariant="normal">Ω</m:mi> <m:mo>,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign="left"> <m:mo>−</m:mo> <m:mi mathvariant="normal">Δ</m:mi> <m:mi>ϕ</m:mi> <m:mo>=</m:mo> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mi>u</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mi>q</m:mi> </m:mrow> </m:msup> <m:mspace width="1.0em"/> </m:mtd> <m:mtd columnalign="left"> <m:mstyle> <m:mspace width="0.1em"/> <m:mtext>in</m:mtext> <m:mspace width="0.1em"/> </m:mstyle> <m:mspace width="0.33em"/> <m:mi mathvariant="normal">Ω</m:mi> <m:mo>,</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd columnalign="left"> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mi>ϕ</m:mi> <m:mo>=</m:mo> <m:mn>0</m:mn> <m:mspace width="1.0em"/> </m:mtd> <m:mtd columnalign="left"> <m:mstyle> <m:mspace width="0.1em"/> <m:mtext>on</m:mtext> <m:mspace width="0.1em"/> </m:mstyle> <m:mspace width="0.33em"/> <m:mo>∂</m:mo> <m:mi mathvariant="normal">Ω</m:mi> <m:mo>,</m:mo> </m:mtd> </m:mtr> </m:mtable> </m:mrow> </m:mfenced> </m:math> \left\{\begin{array}{ll}-\left(a+b\mathop{\displaystyle \int }\limits_{\Omega }{| \nabla u| }^{p}{\rm{d}}x\right){\Delta }_{p}u+\phi {| u| }^{q-2}u=\lambda {u}^{-\gamma }+{| u| }^{{p}^{\ast }-2}u\hspace{1.0em}&amp; \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ -\Delta \phi ={| u| }^{q}\hspace{1.0em}&amp; \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}\Omega ,\\ u=\phi =0\hspace{1.0em}&amp; \hspace{0.1em}\text{on}\hspace{0.1em}\hspace{0.33em}\partial \Omega ,\end{array}\right. where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="normal">Ω</m:mi> </m:math> \Omega is a bounded domain in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> </m:math> {{\mathbb{R}}}^{N} with Lipschitz boundary <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mo>∂</m:mo> <m:mi mathvariant="normal">Ω</m:mi> </m:math> \partial \Omega , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mn>0</m:mn> <m:mo>&lt;</m:mo> <m:mi>γ</m:mi> <m:mo>&lt;</m:mo> <m:mn>1</m:mn> </m:math> 0\lt \gamma \lt 1 , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>Δ</m:mi> </m:mrow> <m:mrow> <m:mi>p</m:mi> </m:mrow> </m:msub> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mi mathvariant="normal">div</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mrow> <m:mo>∇</m:mo> </m:mrow> <m:mi>u</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mi>p</m:mi> <m:mo>−</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mrow> <m:mo>∇</m:mo> </m:mrow> <m:mi>u</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {\Delta }_{p}u={\rm{div}}\left({| \nabla u| }^{p-2}\nabla u) , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mn>1</m:mn> <m:mo>&lt;</m:mo> <m:mi>p</m:mi> <m:mo>&lt;</m:mo> <m:mi>q</m:mi> <m:mo>&lt;</m:mo> <m:mfrac> <m:mrow> <m:msup> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mo>*</m:mo> </m:mrow> </m:msup> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:mfrac> </m:math> 1\lt p\lt q\lt \frac{{p}^{* }}{2} , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi>p</m:mi> </m:mrow> <m:mrow> <m:mo>*</m:mo> </m:mrow> </m:msup> <m:mo>=</m:mo> <m:mi>N</m:mi> <m:mi>p</m:mi> <m:mo>⁄</m:mo> <m:mi>N</m:mi> <m:mo>−</m:mo> <m:mi>p</m:mi> </m:math> {p}^{* }=Np/N-p is the critical Sobolev exponent, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>λ</m:mi> <m:mo>&gt;</m:mo> <m:mn>0</m:mn> </m:math> \lambda \gt 0 . With the Nehari manifold approach, the above problem is discovered to have at least one weak solution. Furthermore, the singular term and critical nonlinearity arise concurrently, which is the main innovation and difficulty of this article. To some extent, we generalize the previous results.

Baoling Yang

Deli Zhang

Sihua Liang

On Kirchhoff-Schrödinger-Poisson-type systems with singular and critical nonlinearity

关于具有奇异和临界非线性的Kirchhoff-Schrödinger-Poisson型系统

Abstract Considering the prevalence of asymptomatic individuals during the spread of disease, this article develops a model of degenerate reaction diffusion Cholera with asymptomatic individuals. First, the well-posedness of model is studied, including the global existence of solutions and the existence of attractor. Second, the basic reproduction number <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi class="MJX-tex-caligraphic" mathvariant="script">ℛ</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> </m:msub> </m:math> {{\mathcal{ {\mathcal R} }}}_{0} is defined to determine whether the disease is vanishing or persistent. In particular, we also analyze the asymptotic behavior of the endemic steady state when the diffusion rate of susceptible or asymptomatic individuals tends to 0 or infinity. Finally, by fitting the theoretical results with some numerical simulations, we find that the spatial distribution of disease and local epidemic risk are less affected by the mobility of susceptible populations, whereas the mobility of asymptomatic or symptomatic populations significantly affects the spatial and temporal distribution of infected populations. In addition, we found that the proportion of asymptomatic individuals to infected individuals is also a key factor in disease epidemics, and how to quickly diagnose asymptomatic individuals for disease control and prevention should be of a particular concern.

Shengfu Wang

Linfei Nie

Global stability and asymptotic profiles of a partially degenerate reaction diffusion Cholera model with asymptomatic individuals

全球稳定性与渐近特征：具有无症状个体的部分退化反应扩散霍乱模型

Abstract We study heat equations with generalized fractional Laplacian, which is defined by the spectral theory. Here we develop the existence theory for those equations. Also, we present some numerical simulations for our problems.

Igor Kossowski

Bogdan Przeradzki

Nonlocal heat equations with generalized fractional Laplacian

带有广义分数阶拉普拉斯算子的非局部热方程

Abstract In this article, we are concerned with the existence of nontrivial solutions to the Choquard equation <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:mo>−</m:mo> <m:mi mathvariant="normal">Δ</m:mi> <m:mi>u</m:mi> <m:mo>+</m:mo> <m:mi>α</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mi>x</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mo>−</m:mo> <m:mi>μ</m:mi> </m:mrow> </m:msup> <m:mo>∗</m:mo> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mi>u</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mi>q</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mi>u</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mi>q</m:mi> <m:mo>−</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mi>u</m:mi> <m:mspace width="1.0em"/> <m:mstyle> <m:mspace width="0.1em"/> <m:mtext>in</m:mtext> <m:mspace width="0.1em"/> </m:mstyle> <m:mspace width="0.33em"/> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> <m:mspace width="1em"/> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>N</m:mi> <m:mo>≥</m:mo> <m:mn>2</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> </m:math> -\Delta u+\alpha \left(x)u=\left({| x| }^{-\mu }\ast {| u| }^{q}){| u| }^{q-2}u\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N}\hspace{1em}\left(N\ge 2), with recurrent potential <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>α</m:mi> </m:math> \alpha , where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mn>0</m:mn> <m:mo>&lt;</m:mo> <m:mi>μ</m:mi> <m:mo>&lt;</m:mo> <m:mi>N</m:mi> </m:math> 0\lt \mu \lt N and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mfrac> <m:mrow> <m:mn>2</m:mn> <m:mi>N</m:mi> <m:mo>−</m:mo> <m:mi>μ</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:mfrac> <m:mo>&lt;</m:mo> <m:mi>q</m:mi> <m:mo>&lt;</m:mo> <m:mfrac> <m:mrow> <m:mn>2</m:mn> <m:mi>N</m:mi> <m:mo>−</m:mo> <m:mi>μ</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> <m:mo>−</m:mo> <m:mn>2</m:mn> </m:mrow> </m:mfrac> </m:math> \frac{2N-\mu }{N}\lt q\lt \frac{2N-\mu }{N-2} . Our results include some classical cases where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>α</m:mi> </m:math> \alpha is constant and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>α</m:mi> </m:math> \alpha is periodic, as well as some new cases, such as <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>α</m:mi> </m:math> \alpha being almost periodic and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>α</m:mi> </m:math> \alpha being only bounded and uniformly continuous.

Hui-Sheng Ding

Quan Liu

Wei Long

Lan Zhong

Choquard equations with recurrent potentials

具有递归势的Choquard方程

Abstract In this article, we investigate the general qusi-one-dimensional nozzle flows governed by non-isentropic compressible Euler system. First, the steady states of the subsonic and supersonic flows are analyzed. Then, the existence, stability, and uniqueness of the subsonic temporal periodic solutions around the steady states are proved by constructing a new iterative format technically. Besides, further regularity and stability of the obtained temporal periodic solutions are obtained, too. The main difficulty in the proof is coming from derivative loss, which is caused by the diagonalization. Observing that the entropy is conserved along the second characteristic curve, we overcome this difficulty by transforming the derivative of entropy with respect to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>x</m:mi> </m:math> x into a derivative along the direction of first or third characteristic. The results demonstrate that dissipative boundary feedback control can stabilize the non-isentropic compressible Euler equations in qusi-one-dimensional nozzles.

Abbreviation	Adv. Nonlinear Anal.
Journal Impact	3.12
Quartiles(Global)	MATHEMATICS, APPLIED(Q1)

ISSN	2191-9496, 2191-950X
h-index	36
Top Journals	Yes

Publication Information	Publisher: De Gruyter Open Ltd.，Publishing cycle: ，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 2012，Proportion of original research papers: 100.00%，Self Citation Rate:6.20%， Gold OA Rate: 97.35%
Journal Fees	$Details
Average review cycle	网友分享经验：30 Weeks

Advances in Nonlinear Analysis

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On Kirchhoff-Schrödinger-Poisson-type systems with singular and critical nonlinearity

Global stability and asymptotic profiles of a partially degenerate reaction diffusion Cholera model with asymptomatic individuals

Nonlocal heat equations with generalized fractional Laplacian

Choquard equations with recurrent potentials

Temporal periodic solutions of non-isentropic compressible Euler equations with geometric effects

On Kirchhoff-Schrödinger-Poisson-type systems with singular and critical nonlinearity

Global stability and asymptotic profiles of a partially degenerate reaction diffusion Cholera model with asymptomatic individuals

Nonlocal heat equations with generalized fractional Laplacian

Choquard equations with recurrent potentials

Temporal periodic solutions of non-isentropic compressible Euler equations with geometric effects