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Pain and depression comorbidity (PD) among older adults in China is common and significantly affects their physical and mental health. The psychosocial factors may affect people's feelings, understanding and expression of pain and depression, leading to inaccurate assessment of this condition. Educational attainment is thought to be associated with either pain or depression. However, we do not yet know the relationship between educational attainment and PD. Using data from the 2018 China Health and Retirement Longitudinal Study in 2018, we analyzed various variables in 7742 individuals aged 60 years and older. Our results indicate significant differences between the PD and non-PD populations in terms of social, lifestyle, and behavioral factors. We observed a significant decrease in the incidence of PD among older adults with higher levels of education (p

Abstract Background Few studies have investigated factors associated with anxiety and depression among patients with erectile dysfunction (ED). This study aimed to investigate associated factors and the prevalence of anxiety and depression in this special group in China. Methods Data from 511 patients with ED aged 18–60 years were collected between July 2021 and April 2022. The 5-item International Index of Erectile Function (IIEF-5) questionnaire, self-rating anxiety scale (SAS) and self-rating depression scale (SDS) were used to evaluate erectile function, anxiety and depression, respectively. Univariate analysis and multivariate linear regression analyses were used to explore the associated factors of depression and anxiety. Results The prevalence of anxiety and depression among ED patients was 38.16% and 64.97%, respectively. The mean anxiety index score was 47.37 ± 6.69 points, and the mean depression index was 54.72 ± 9.10 points. Multiple linear regression analysis showed that worse ED, low education level, and smoking were positively associated with increased risk of anxiety and depression. In addition, younger age, longer onset time, and irregular sleep were positively associated with high risk of anxiety, and irregular exercise was associated with severe depression. Conclusions The prevalence of depression and anxiety in ED patients is high, and the severity of ED, age, education level, smoking, onset time, regular sleep, and exercise were associated with anxiety or depression. Reversible risk factors should be avoided and individualized psychological support services are necessary for ED patients.

We consider the existence of rotating solitary waves (vortices) for a coupled Schrodinger equations by finding solutions to the singular system $$\displaylines{ -\Delta u+\lambda_1 u+\frac{u}{|x|^2}=\mu_1 u^3+\beta u v^2, \quad x\in\mathbb{R}^2, \cr -\Delta v+\lambda_2 v+\frac{v}{|x|^2}=\mu_2 v^3+\beta u^2 v, \quad x\in\mathbb{R}^2, \cr u,v \geq 0,\quad x\in\mathbb{R}^2, }$$ where $\lambda_1,\lambda_2,\mu_1, \mu_2$ are positive parameters, $\beta\neq 0$. We show that this system has a positive least energy solution for the cases When either $\beta$ is negative or \beta is positive and small or large. Moreover, if $\lambda_1=\lambda_2$, then the solution is unique. We also study the limiting behavior of the least energy solutions in the repulsive case for $\beta\to-\infty$, and phase separation.

ABSTRACT: Introduction: There are many Western reports on factors influencing coital frequency among men. However, no articles could be found about the factors influencing sexual activity among Chinese men. Aim: The aim of this study was to identify the factors that influence the coital frequency of Chinese men. Main Outcome Measures: The main outcome measures included self-reported monthly coital frequency, age, occupation, education level, andrology-related scales and dietary habits. Methods: Data for 1,407 men aged 18–79 years were collected in the Health Management Center of the Third Xiangya Hospital of Central South University from January 2019 to May 2019. The respondents completed the questionnaires independently or with the help of an interviewer (who read or explained the questionnaires to them) to analyse the factors that influence coital frequency. Results: In the previous 6 months, the sample had a mean monthly coital frequency (±SD) of 4.34 ± 3.18. Univariate logistic regression results indicated that the number of children (P = 0.004), IIEF-5 scores (P

MicroRNA (miRNA)–gene interactions are well-recognized as involved in the progression of almost all cancer types including prostate cancer, which is one of the most common cancers in men. This study explored the significantly dysregulated genes and miRNAs and elucidated the potential miRNA–gene regulatory network in prostate cancer. Integrative analysis of prostate cancer and normal prostate transcriptomic data in The Cancer Genome Atlas dataset was conducted using both differential expression analysis and weighted correlation network analysis (WGCNA). Thirteen genes (RRM2, ORC6, CDC45, CDKN2A, E2F2, MYBL2, CCNB2, PLK1, FOXM1, CDC25C, PKMYT1, GTSE1, and CDC20) were potentially correlated with prostate cancer based on functional enrichment analyses. MiRNAs targeting these genes were predicted and eight miRNAs were intersections between those miRNAs and the hub miRNAs obtained from miRNA WGCNA analysis. Three genes (E2F2, RRM2, and PKMYT1) and four miRNAs (hsa-mir-17-5p, hsa-mir-20a-5p, hsa-mir-92a-3p, and hsa-mir-93-5p) were key factors according to the interaction network. RRM2 and PKMYT1 were significantly related to survival. These findings partially elucidated the dysregulation of gene expressions in prostate cancer. Efficient manipulations of the miRNA–gene interactions in prostate cancer may be exploited as promising therapeutics.

In this article, we consider the existence of multiple nodal solutions of the nonlinear Choquard equation $$\displaylines{ -\Delta u+u=(|x|^{-1}\ast|u|^p)|u|^{p-2}u \quad \text{in }\mathbb{R}^3,\cr u\in H^1(\mathbb{R}^3), }$$ where $p\in (5/2,5)$. We show that for any positive integer k, the above problem has at least one radially symmetrical solution changing sign exactly k-times.

In this article, we consider the existence of nodal solutions for the Schrodinger-Poisson type problem \begin{gather*} -\Big(a+b\int_{\mathbb{R}^3}|\nabla u|^2\,dx\Big)\Delta u+V(|x|)u+\varphi u =|u|^{p-2}u,\quad\text{in }\mathbb{R}^3, \\ -\Delta\varphi=u^2, \quad \lim_{|x|\to \infty}\varphi (x) =0, \end{gather*} where $a, b$ are positive constants, $p\in(4,6)$ and $ V(x)$ is a radial smooth function. For each $k\in \mathbb{N}_+$, we show the existence of to nodal solution changing sign exactly $k$ times.

In this article, we consider the existence of solutions of the critical problem with a Hardy term for fractional Laplacian $$\displaylines{ (-\Delta)^s u -\mu \frac u{|x|^{2s}}= u^{2^*_s-1} \quad \text{in }\Omega,\cr u>0 \quad \text{in }\Omega, \cr u=0 \quad \text{on }\partial \Omega, }$$ where $\Omega\subset \mathbb{R}^N$ is a smooth bounded domain and $0\in\Omega$, $\mu$ is a positive parameter, $N>2s$ and $s\in(0,1)$, $2^*_{s} =\frac{2N}{N-2s}$ is the critical exponent. $(-\Delta)^s$ stands for the spectral fractional Laplacian. Assuming that $\Omega$ is non-contractible, we show that there exists $\mu_0>0$ such that $0

This article concerns the existence of positive solutions to the nonlinear elliptic system involving critical Hardy-Sobolev exponent $$displaylines{ -Delta u= frac{2lambdaalpha}{alpha+eta} frac{u^{alpha-1} v^eta}{|pi(x)|^s}- u^p, quad hbox{in } Omega,cr -Delta v= frac{2lambdaeta}{alpha+eta} frac{u^alpha v^{eta-1}}{|pi(x)|^s}- v^p, quad hbox{in } Omega,cr u>0,quad v>0, quad hbox{in } Omega,cr u=v=0, quad hbox{on } partialOmega, }$$ where $Ngeq 4$ and $Omega$ is a $C^1$ bounded domain in $mathbb{R}^N$, $01$, $lambda>0$ and $1leq p

In this paper, we are concerned with the existence of positive solutions of the following nonlinear elliptic system involving critical Hardy-Sobolev exponent \begin{equation*}\label{eq:1}(*) \left\{ \begin{array}{lll} -\Delta u= \frac{2\alpha}{\alpha+\beta}\frac{u^{\alpha-1}v^\beta}{|x|^s}-\lambda u^p, & \quad {\rm in}\quad \Omega,\\[2mm] -\Delta v= \frac{2\beta}{\alpha+\beta}\frac{u^\alpha v^{\beta-1}}{|x|^s}-\lambda v^p, & \quad {\rm in}\quad \Omega,\\[2mm] u\gt 0, v\gt 0, &\quad {\rm in}\quad \Omega,\\[2mm] u=v=0, &\quad {\rm on}\quad \partial\Omega, \end{array} \right. \end{equation*} where \(N\geq 4\) and \(\Omega\) is a \(C^1\) bounded domain in \(\mathbb{R}^N\) with \(0\in\partial\Omega\). \(0\lt s \lt 2\), \(\alpha+\beta=2^*(s)=\frac{2(N-s)}{N-2}\), \(\alpha,\beta\gt 1\), \(\lambda\gt 0\) and \(1 \lt p\lt \frac{N+2}{N-2}\). The case when 0 belongs to the boundary of \(\Omega\) is closely related to the mean curvature at the origin on the boundary. We show in this paper that problem \((*)\) possesses at least a positive solution.

In this article, we consider the regularity and symmetry of positive solutions to the nonlinear integral system $$ u(x)=int_{mathbb{R}^n}K_{alpha}(x-y)frac{v(y)^q}{|y|^eta},dy, quad v(x)=int_{mathbb{R}^n}K_{alpha}(x-y)frac{u(y)^p}{|y|^eta},dy $$ for $xin mathbb{R}^n$, where $K_alpha(x)$ is the kernel of the operator $(- Delta)^{alpha}+ id$ of order $alpha$, with $0leq etafrac{n-2alpha+eta}{n}. $$ We show that positive solution pairs $(u,v)in L^{p+1}(mathbb{R}^n)imes L^{q+1}(mathbb{R}^n)$ are locally Holder continuous in $mathbb{R}^Nsetminus{0}$, radially symmetric about the origin, and strictly decreasing.

This paper is concerned with ground state solutions for the Hénon type equation \(-\Delta u(x)=|y|^{\alpha} u^{p-1}(x)\) in \(\Omega\), where \(\Omega=B^k(0,1)\times B^{n-k}(0,1)\subset \mathbb{R}^n\) and \(x=(y,z) \in \mathbb{R}^k \times \mathbb{R}^{n-k}\). We study the existence of cylindrically symmetric and non-cylindrically symmetric ground state solutions for the problem. We also investigate asymptotic behavior of the ground state solution when \(p\) tends to the critical exponent \(2^*=\frac {2n}{n-2}\) if \(n\geq 3\).

In this article, we investigate the asymptotic behavior of positive ground state solutions, as $alphaoinfty$, for the following Henon type system $$ -Delta u=frac{2p}{p+q}|x|^alpha u^{p-1}v^q,quad -Delta v=frac{2q}{p+q}|x|^alpha u^pv^{q-1},quad hbox{in } B_1(0) $$ with zero boundary condition, where $B_1(0)subsetmathbb{R}^N$ ($Ngeq3$) is the unit ball centered at the origin, $p,q>1$, $p+q

Let $(mathcal{M}, g)$ be a compact, connected, orientable, Riemannian $n$-manifold of class $C^{infty}$ with Riemannian metric $g$ $(ngeq 3)$. We study the existence of solutions to the equation $$ -varepsilon^2Delta_{g} u+V(x)u=K(x)|u|^{p-2}u $$ on this Riemannian manifold. Here $2

In this paper, we investigate the Neumann problem for a critical elliptic system in exterior domains. Assuming that the coefficient $Q(x)$ is a positive smooth function and $lambda$, $mugeq0$ are parameters, we examine the common effect of the mean curvature of the boundary $partial Omega $ and the shape of the graph of the coefficient $Q(x)$ on the existence of the least energy solutions.

In this paper, we study the existence of solutions for the nonlinear elliptic system $$displaylines{ -Delta u+u=|u|^{p-1}u+lambda v quad hbox{in } Omega, cr -Delta v+v=|v|^{p-1}v+lambda u quad hbox{in } Omega, cr u=v=0 quad hbox{on } partialOmega, }$$ where $Omega$ is a exterior domain in $mathbb{R}^N$, $Ngeq 3$. We show that the system possesses at least one nontrivial positive solution.

In this paper, we show the existence of solutions for the strongly indefinite elliptic system $$displaylines{ -Delta u=lambda u+f(x,v) quadhbox{in }Omega, cr -Delta v=lambda v+g(x,u) quadhbox{in }Omega, cr u=v=0, quadhbox{on }partialOmega, }$$ where $Omega$ is a bounded domain in $mathbb{R}^N; (Ngeq 3)$ with smooth boundary, $lambda_{k_0}

In this paper we present a novel variational approach to the question of existence and multiplicity of positive solutions to semipositone problems in a bounded smooth domain of $mathbb{R}^N$. We consider both the sublinear and superlinear cases.

We establish an existence result for strongly indefinite semilinear elliptic systems in R^N.