Results 71 to 80 of about 3,531,413 (264)

Normalized solutions for critical Schrödinger equations involving (2,q)-Laplacian [PDF]

Opuscula Mathematica
In this paper, we consider the following critical Schrödinger equation involving \((2,q)\)-Laplacian: \[\begin{cases} -\Delta u-\Delta_{q} u=\lambda u+\mu |u|^{\gamma-2}u+|u|^{2^*-2}u \quad\text{in }\mathbb{R}^N, \\ \int_{\mathbb{R}^N} |u|^{2}dx=a^2,\end{
Lulu Wei, Yueqiang Song
doaj   +1 more source

Translating whole‐genome doubling into precision medicine in cancer

Molecular Oncology, EarlyView.
Whole‐genome doubling creates a WGD‐positive tumor state characterized by persistent chromosomal instability, karyotypic diversification, and cellular stress. These same biological pressures drive aggressive tumor evolution while exposing therapeutic vulnerabilities, providing a rationale for WGD‐informed precision medicine. Whole‐genome doubling (WGD)
Sejung Lee, Junghyeok Lim, Jinhyuk Bhin
wiley   +1 more source

Multiplicity of solutions to a p-Kirchhoff equation with critical exponent

Boundary Value Problems
In this paper, we consider the following p-Kirchhoff equation: P { [ M ( ∥ u ∥ p ) ] p − 1 ( − Δ p u + | u | p − 2 u ) = λ f ( x , u ) + | u | p ∗ − 2 u in Ω , u = 0 , on ∂ Ω , $$ \left \{ \textstyle\begin{array}{l@{\quad}l} [M(\|u\|^{p})]^{p-1}\left ...
Zhaomin Jiang
doaj   +1 more source

Existence of solutions for a doubly critical Schrödinger-Poisson system on the first Heisenberg group [PDF]

Opuscula Mathematica
This work is devoted to the study of a class of Schrödinger-Poisson system with doubly critical growth on the first Heisenberg group. Utilizing the concentration-compactness principle associated with classical Sobolev space on the Heisenberg group and ...
Xueyan Ma, Shaoyun Shi, Yueqiang Song
doaj   +1 more source

Single‐cell DNA methylation profiling: Technologies, computation, and applications in precision oncology

Molecular Oncology, EarlyView.
Single‐cell DNA methylation (scDNAme) profiling maps epimutational clonal evolution, revealing mechanisms of malignancy and therapeutic resistance across diverse cancer types. By providing a high‐resolution landscape of intratumoral heterogeneity, these technologies empower precise patient stratification, guide the development of enhanced ...
Ik Soo Kim
wiley   +1 more source

Targeting transcription factors associated with hemoglobinopathies: Lessons from successful interventions and implications for cancer

Molecular Oncology, EarlyView.
This review summarizes the transcription factors, repressive chromatin‐modifying complexes, and epigenetic mechanisms that control fetal hemoglobin repression. Notably, many regulators of γ‐globin silencing also function in transcriptional and epigenetic networks that drive cancer, highlighting opportunities to translate advances in hemoglobinopathy ...
Meigen Yu, Puspa Das, Xing Zhang, Xiaodong Cheng   +3 more
wiley   +1 more source

Fractional elliptic problems with two critical Sobolev-Hardy exponents

Electronic Journal of Differential Equations, 2018
By using the mountain pass lemma and a concentration compactness principle, we obtain the existence of positive solutions to the fractional elliptic problem with two critical Hardy-Sobolev exponents at the origin.
Wenjing Chen
doaj  

Infinitely many solutions for the p-fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity

Nonlinear Analysis, 2018
In this paper, we consider the fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity. By means of the concentration-compactness principle in fractional Sobolev space and the Kajikiya's new version of the symmetric mountain ...
Sihua Liang, Jihui Zhang
doaj   +1 more source

Concentration-compactness principle for mountain pass problems

, 2005
In the paper we show that critical sequences associated with the mountain pass level for semilinear elliptic problems on $\R^N$ converge when the non-linearity is subcritical, superlinear and satisfies the penalty condition $F_\infty(s)
openaire   +2 more sources

Spatial biology in cancer epigenetics

Molecular Oncology, EarlyView.
Spatial epigenomics combines molecular profiling with tissue architecture to reveal how gene regulation is organized within intact tissues. In cancer, these technologies uncover the mechanisms driving tumor heterogeneity and microenvironmental interactions, opening new opportunities for biomarker discovery and precision medicine.
Eva Crespo‐García, Manel Esteller
wiley   +1 more source