Results 61 to 70 of about 11,870,254 (353)
Existence of positive solutions to perturbed nonlinear Dirichlet problems involving critical growth
Electronic Journal of Differential Equations, 2017 We consider the following perturbed nonlinear elliptic problem with critical growth $$\displaylines{ -\varepsilon^2\Delta u+V(x)u=f(x)|u|^{p-2}u +\frac{\alpha}{\alpha+\beta}K(x)|u|^{\alpha-2}u|v|^\beta,\quad x\in \mathbb{R}^N,\cr -\varepsilon^2 ...
Huixing Zhang, Ran Zhang
doaj
Decoding the dual role of autophagy in cancer through transcriptional and epigenetic regulation
FEBS Letters, EarlyView.Transcriptional and epigenetic regulation controls autophagy, which exerts context‐dependent effects on cancer: Autophagy suppresses tumorigenesis by maintaining cellular homeostasis or promotes tumor progression by supporting survival under stress. In this “In a Nutshell” article, we explore the intricate mechanisms of the dual function of autophagy ...
Young Suk Yu, Ik Soo Kim, Sung Hee Baek
wiley +1 more source
Sign-changing solutions for Schrödinger system with critical growth
Electronic Research Archive, 2022 We consider the following Schrödinger system $ \begin{equation*} \left\{ \begin{aligned} &-\Delta u_j = \sum\limits_{i = 1}^k \beta_{ij}|u_i|^3|u_j|u_j+\lambda_j|u_j|^{q-2}u_j, \ \ \ \text{in}\, \, \Omega, \\ &u_j = 0\quad\text{on ...
Changmu Chu +2 more
doaj +1 more source
Autophagy in cancer and protein conformational disorders
FEBS Letters, EarlyView.Autophagy plays a crucial role in numerous biological processes, including protein and organelle quality control, development, immunity, and metabolism. Hence, dysregulation or mutations in autophagy‐related genes have been implicated in a wide range of human diseases.
Sergio Attanasio
wiley +1 more source
Double phase anisotropic variational problems involving critical growth
Advances in Nonlinear AnalysisIn this study, we investigate some existence results for double phase anisotropic variational problems involving critical growth. We first establish a Lions-type concentration-compactness principle and its variant at infinity for the solution space ...
Ho Ky, Kim Yun-Ho, Zhang Chao
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AIMS MathematicsIn this paper, we study the following Kirchhoff-type equation:$ \begin{equation*} M\left(\displaystyle{\int}_{\mathbb{R}^2}(|\nabla u|^2 +u^2)\mathrm{d} x\right)(-\Delta u+u) + \mu V(x)u = K(x) f(u) \ \ \mathrm{in} \ \ \mathbb{R}^2, \end{equation ...
Zhenluo Lou , Jian Zhang
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A stepwise emergence of evolution in the RNA world
FEBS Letters, EarlyView.How did biological evolution emerge from chemical reactions? This perspective proposes a gradual scenario of self‐organization among RNA molecules, where catalytic feedback on random mixtures plays the central role. Short oligomers cross‐ligate, and self‐assembly enables heritable variations. An event of template‐externalization marks the transition to
Philippe Nghe
wiley +1 more source
Fractional elliptic systems with nonlinearities of arbitrary growth
Electronic Journal of Differential Equations, 2017 In this article we discuss the existence, uniqueness and regularity of solutions of the following system of coupled semilinear Poisson equations on a smooth bounded domain $\Omega$ in $\mathbb{R}^n$: $$\displaylines{ \mathcal{A}^s u= v^p \quad\text ...
Edir Junior Ferreira Leite
doaj
FEBS Letters, EarlyView.The enzyme 5‐lipoxygenase (5‐LOX) catalyzes the first step in the biosynthesis of leukotrienes (LTs) involved in inflammatory pathophysiology. After cellular stimulation, 5‐LOX translocates to the nucleus, interacting with the 5‐LOX‐activating protein (FLAP) to form LTA4 from arachidonic acid (AA).
Erik Romp +5 more
wiley +1 more source
Open MathematicsIn this article, we investigate the following nonlinear Kirchhoff equation with Sobolev critical growth: −a+b∫R3∣∇u∣2dxΔu+λu=μf(u)+∣u∣4u,inR3,u>0,∫R3∣u∣2dx=m2,inR3,(Pm)\left\{\begin{array}{l}-\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R ...
Zhang Shiyong, Zhang Qiongfen
doaj +1 more source