Global bifurcation of positive solutions for a superlinear $p$-Laplacian system by Lijuan Yang, Ruyun Ma

“…We are concerned with the principal eigenvalue of \begin{equation*} \begin{cases} -\Delta_p u= \lambda\theta_1\varphi_p(v), &x\in \Omega,\\ -\Delta_p v= \lambda\theta_2\varphi_p(u), &x\in \Omega,\\ u=0=v,\ &x\in\partial\Omega \end{cases} \tag{P} \end{equation*} and the global structure of positive solutions for the system \begin{equation*} \begin{cases} -\Delta_p u= \lambda f(v), &x\in \Omega,\\ -\Delta_p v= \lambda g(u), &x\in \Omega,\\ u=0=v,\ &x\in\partial\Omega, \end{cases} \tag{Q} \end{equation*} where $\varphi_p(s)=|s|^{p-2}s$, $\Delta_p s=\text{div}(|\nabla s|^{p-2}\nabla s)$, $\lambda>0$ is a parameter, $\Omega\subset\mathbb{R}^N$, $N> 2$, is a bounded domain with smooth boundary $\partial\Omega$, $f,g:\mathbb{R}\to(0,\infty)$ are continuous functions with $p$-superlinear growth at infinity. …”
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Analysis of global dynamics in an attraction-repulsion model with nonlinear indirect signal and logistic source by Chang-Jian Wang, Jia-Yue Zhu

“…The following chemotaxis system has been considered: \begin{document}$ \begin{equation*} \left\{ \begin{array}{ll} v_{t} = \Delta v-\xi \nabla\cdot(v \nabla w_{1})+\chi \nabla\cdot(v \nabla w_{2})+\lambda v-\mu v^{\kappa},\ &\ \ x\in \Omega, \ t>0,\\[2.5mm] w_{1t} = \Delta w_{1}-w_{1}+w^{\kappa_{1}}, \ 0 = \Delta w-w+v^{\kappa_{2}}, \ &\ \ x\in \Omega, \ t>0,\\[2.5mm] 0 = \Delta w_{2}-w_{2}+v^{\kappa_{3}}, \ &\ \ x\in \Omega, \ t>0 , \end{array} \right. …”
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Schrödinger–Hardy system without the Ambrosetti–Rabinowitz condition on Carnot groups by Wenjing Chen, Fang Yu

“…In this paper, we study the following Schrödinger–Hardy system \begin{equation*} \begin{cases} -\Delta_{\mathbb{G}}u-\mu\frac{\psi^2}{r(\xi)^2}u=F_u(\xi,u,v)\ &{\rm in}\ \Omega, \\ -\Delta_{\mathbb{G}}v-\nu\frac{\psi^2 }{r(\xi)^2}v=F_v(\xi,u,v)\ &{\rm in}\ \Omega, \\ u=v=0 \ \ & {\rm on}\ \partial\Omega, \end{cases} \end{equation*} where $\Omega $ is a smooth bounded domain on Carnot groups $\mathbb{G}$, whose homogeneous dimension is $Q\geq 3$, $\Delta_{\mathbb{G}}$ denotes the sub-Laplacian operator on $\mathbb{G}$, $\mu$ and $\nu$ are real parameters, $r(\xi)$ is the natural gauge associated with fundamental solution of $-\Delta_{\mathbb{G}}$ on $\mathbb{G}$, $\psi$ is the geometrical function defined as $\psi=|\nabla_{\mathbb{G}}r|$, and $\nabla_{\mathbb{G}}$ is the horizontal gradient associated with $\Delta_{\mathbb{G}}$. …”
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Boundedness and large time behavior of a signal-dependent motility system with nonlinear indirect signal production by Ya Tian, Jing Luo

“…In this paper, we study a chemotaxis system with nonlinear indirect signal production \begin{document}$ \left\{ {\begin{array}{*{20}{l}} {{u_t} = \Delta \left( {\gamma \left( v \right) u } \right)}+ru-\mu u^l, \quad &x\in \Omega, t>0, \\ {{v_t} = \Delta v - v + w^{\beta}}, \quad &x\in \Omega, t>0, \\ {{w_t} = - \delta w + u}, \quad &x\in \Omega, t>0, \end{array}} \right. …”
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A note on the global existence and boundedness of an N-dimensional parabolic-elliptic predator-prey system with indirect pursuit-evasion interaction by Liu Ling

“…We investigate the two-species chemotaxis predator-prey system given by the following system: ut=Δu−χ∇⋅(u∇w)+u(λ1−μ1ur1−1+av),x∈Ω,t>0,vt=Δv+ξ∇⋅(v∇z)+v(λ2−μ2vr2−1−bu),x∈Ω,t>0,0=Δw−w+v,x∈Ω,t>0,0=Δz−z+u,x∈Ω,t>0,\left\{\begin{array}{ll}{u}_{t}=\Delta u-\chi \nabla \cdot \left(u\nabla w)+u\left({\lambda }_{1}-{\mu }_{1}{u}^{{r}_{1}-1}+av),& x\in \Omega ,\hspace{0.33em}t\gt 0,\\ {v}_{t}=\Delta v+\xi \nabla \cdot \left(v\nabla z)+v\left({\lambda }_{2}-{\mu }_{2}{v}^{{r}_{2}-1}-bu),& x\in \Omega ,\hspace{0.33em}t\gt 0,\\ 0=\Delta w-w+v,& x\in \Omega ,\hspace{0.33em}t\gt 0,\\ 0=\Delta z-z+u,& x\in \Omega ,\hspace{0.33em}t\gt 0,\end{array}\right. in a bounded domain Ω⊂RN(N≥1)\Omega \subset {{\mathbb{R}}}^{N}\left(N\ge 1) with smooth boundary, where parameters χ,ξ,λi,μi>0\chi ,\xi ,{\lambda }_{i},{\mu }_{i}\gt 0, and ri>1(i=1,2){r}_{i}\gt 1\hspace{0.33em}\left(i=1,2). …”
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Multi-bump solutions of Schrödinger–Bopp–Podolsky system with steep potential well by Li Wang, Jun Wang, Jixiu Wang

“…In this paper, we study the existence of multi-bump solutions for the following Schrödinger–Bopp–Podolsky system with steep potential well: \begin{equation*} \begin{cases} -\Delta u+(\lambda V(x)+V_0(x))u+K(x)\phi u= |u|^{p-2}u, &x\in \mathbb{R}^3,\\ -\Delta \phi+a^2\Delta^2\phi=K(x) u^2, &x\in \mathbb{R}^3, \end{cases} \end{equation*} where $p \in(4,6), a>0$ and $\lambda$ is a parameter. …”
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Global boundedness in a Keller-Segel system with nonlinear indirect signal consumption mechanism by Zihan Zheng, Juan Wang, Liming Cai

“…In this paper, we study a quasilinear chemotaxis model with a nonlinear indirect consumption mechanism$ \begin{equation*} \left\{ \begin{array}{ll} v_{1t} = \nabla \cdot\big(\psi(v_{1})\nabla v_{1}-\chi \phi(v_{1})\nabla v_{2}\big)+\lambda_{1}v_{1}-\lambda_{2}v_{1}^{\beta},\ &\ \ x\in \Omega, \ t>0,\\[2.5mm] v_{2t} = \Delta v_{2}-w^{\theta}v_{2}, \ &\ \ x\in \Omega, \ t>0,\\[2.5mm] 0 = \Delta w-w+v_{1}^{\alpha}, \ &\ \ x\in \Omega, \ t>0 ,\\[2.5mm] \end{array} \right. …”
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Boundedness of classical solutions to a chemotaxis consumption system with signal dependent motility and logistic source by Baghaei, Khadijeh

“…We consider the chemotaxis system: \begin{equation*} {\left\lbrace \begin{array}{ll} u_{t}=\nabla \cdot \big (\gamma (v) \nabla u-u \,\xi (v) \nabla v\big )+\mu \, u(1-u), & x\in \Omega , \ t>0, \\ v_{t}=\Delta v-uv, & x\in \Omega , \ t>0, \end{array}\right.} …”
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Massless limit and conformal soft limit for celestial massive amplitudes by Wei Fan

“…This can be compared with the conformal soft limit in celestial gluon amplitudes, where a singularity $$1/(\Delta -1)$$ 1 / ( Δ - 1 ) arises and the leading contribution comes from the soft energy $$\omega \rightarrow 0$$ ω → 0 . …”
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Blow-up of nonradial solutions to the hyperbolic-elliptic chemotaxis system with logistic source by Baghaei, khadijeh

“…This paper is concerned with the blow-up of solutions to the following hyperbolic-elliptic chemotaxis system: \begin{equation*} {\left\lbrace \begin{array}{ll} u_{t} =-\nabla \cdot (\chi u \nabla v)+g(u), \qquad x\in \Omega , \ t>0,\\ \;\;\; 0 =\Delta v-v+u, \hspace{58.33328pt}x\in \Omega , \ t>0, \end{array}\right.} …”
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Global boundedness of solutions to a chemotaxis consumption model with signal dependent motility and logistic source by Baghaei, Khadijeh

“…This paper deals with the following chemotaxis system: \begin{equation*} {\left\lbrace \begin{array}{ll} u_{t}=\nabla \cdot \big (\gamma (v) \,\nabla u-u \,\xi (v) \,\nabla v\big )+\mu \, u\,(1-u), & x\in \Omega , \ t>0, \\ v_{t}=\Delta v-uv, & x\in \Omega , \ t>0, \end{array}\right.} …”
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Global Solutions for a Nonlocal Problem with Logarithmic Source Term by Eugenio Lapa

“…The current paper discusses the global existence and asymptotic behavior of solutions of the following new nonlocal problem$$ u_{tt}- M\left(\displaystyle \int_{\Omega}|\nabla u|^{2}\, dx\right)\triangle u + \delta u_{t}= |u|^{\rho-2}u \log|u|, \quad \text{in}\ \Omega \times ]0,\infty[,  $$where\begin{equation*}M(s)=\left\{\begin{array}{ll}{a-bs,}&{\text{for}\ s \in [0,\frac{a}{b}[,}\\{0,}&{\text{for}\ s \in [\frac{a}{b}, +\infty[.}…”
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Enhancing Food Security via selecting Superior Camelina (Camelina sativa L.) parents: a positive approach incorporating pheno-morphological traits, fatty acids composition, and Toc... by Amin Ebrahimi, Hamzeh Minaei Chenar, Sajad Rashidi-Monfared, Danial Kahrizi

“…The analysis unveiled that the average content of omega-3, omega-6, and omega-9 fatty acids in the examined lines was approximately 33%, 20%, and 17%, respectively. …”
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Path Planning For A Mobile Robot Using The Chessboard Method And Gray Wolf Optimization Algorithm In Static And Dynamic Environments by Ali Hatami Zadeh, Javad Sharifi, Meysam Yadegar

“…Four types of grey wolves, namely alpha, beta, delta, and omega, are employed to simulate the leadership hierarchy. …”
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