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Integrated multi-omic atlas reveals the hierarchy of spatiotemporal regulatory networks of mouse gastrulation. [PDF]

Nat Commun
Yang X, Xie B, Shen P, Chen Y, Li C, Tan F, Yang Y, Yang Y, Song R, Mi P, Liu Z, Wen M, Tam PPL, Suo S, Jing N.   +14 more
europepmc   +1 more source

Nodal Solutions for Supercritical Laplace Equations

, 2016
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AI-Powered Radiotherapy for Resource-Limited Settings: Advancing Cervical and Prostate Cancer Treatment Planning with the Radiation Planning Assistant (RPA)

Netherton TJ, Aggarwal A, Alakayleh Q, Beadle BM, Brooks C, Burger H, Cardenas CE, Celaya A, Chacko S, Chung C, Douglas R, El Basha D, Frank S, Fuentes D, Hassanzadeh C, Helbrow J, Hoskin P, Khan M, Kroiss M, Leone A, Lin L, Mumme R, Nguyen C, Nguyen Q, Olanrewaju A, Parameshwaran J, Pollard-Larkin J, Poenisch F, Shah S, Sosa AJ, Tang C, Yu Z, Zhang L, Court LE.   +33 more
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Localized Nodal Solutions for Schrödinger-Poisson Systems

Acta Mathematica Scientia, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Xing, He, Rui, Liu, Xiangqing
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Nodal solutions for anisotropic \((p, q)\)-equations

Nonlinear Analysis: Real World Applications, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zeng, Shengda, Papageorgiou, Nikolaos S.
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Solution of inverse nodal problems

Inverse Problems, 1989
We show that the coefficients in a second-order differential equation can be determined from the positions of the nodes for the eigenfunctions. We prove uniqueness results, derive approximate solutions, give error bounds and present numerical experiments.
Hald, Ole H., McLaughlin, Joyce R.
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Nodal Solutions for Indefinite Robin Problems

Bulletin of the Malaysian Mathematical Sciences Society, 2017
Given a bounded domain \(\Omega \subseteq \mathbb{R}^N\) with a \(C^2\)-boundary, the authors study semilinear Robin problems of the form \[ \begin{cases} -\Delta u(z)+\xi(z)u(z) = f(z,u(z)) &\text{in }\Omega,\\ \frac{\partial u}{\partial n}+\beta(z)u=0 &\text{on }\partial \Omega, \end{cases} \] where the potential function \(\xi\) belongs to \(L^s ...
Filippakis, Michael, Papageorgiou, Nikolaos S.   +1 more
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Nodal solutions of -Laplacian equations

Nonlinear Analysis: Theory, Methods & Applications, 2007
The aim of this paper is to study the existence of nodal radial solutions for the \(p(x)\)-Laplacian equation of the form \[ \begin{gathered} -\text{div}(|\nabla |^{p(x)-2}\nabla u)+ a(x)|u|^{p(x)-2} u=|u|^{q(x)- 2} u\quad\text{in }\Omega,\\ u\in W^{1,p(x)}_0(\Omega).\end{gathered}\tag{1} \] Using a variational method, the authors prove that, for any ...
Fan, Xianling, Zhao, Yuanzhang
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Nodal solutions of a p-Laplacian equation

Proceedings of the London Mathematical Society, 2005
Summary: We prove that the \(p\)-Laplacian problem \(-\Delta_p u = f(x, u)\), with \(u \in W_0^{1,p}(\Omega)\) on a bounded domain \(\Omega \subset \mathbb R^N\), with \(p > 1\) arbitrary, has a nodal solution provided that \(f : \Omega\times\mathbb R \to \mathbb R\) is subcritical, and \(f(x, t) / |t|^{p-2}\) is superlinear.
Bartsch, Thomas, Liu, Zhaoli, Weth, Tobias   +2 more
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Multiple nodal solutions for elliptic equations

Nonlinear Analysis: Theory, Methods & Applications, 2004
In the present study the authors obtain multiple sign-changing solutions for nonlinear elliptic equations under weaker conditions (without assuming that the corresponding functional is \(C^2)\), and multiple critical points for invariant functional under group actions.
Qian, Aixia, Li, Shujie
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