The Cortex and the Critical Point [PDF]
, 2022 How the cerebral cortex operates near a critical phase transition point for optimum performance. Individual neurons have limited computational powers, but when they work together, it is almost like magic.
Beggs, John M.
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Nonlinear Periodic Systems with the p-Laplacian: Existence and Multiplicity Results
Abstract and Applied Analysis, 2007 We study second-order nonlinear periodic systems driven by the vector p-Laplacian with a nonsmooth, locally Lipschitz potential function. Under minimal and natural hypotheses on the potential and using variational methods based on the nonsmooth critical ...
Francesca Papalini
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Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we study the following fractional Kirchhoff type equation \begin{equation*} \begin{cases} \left(a+b\displaystyle\int_{\mathbb{R}^N}\int_{\mathbb{R}^N}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right)(-\Delta)_p^su=|u|^{q-2}u\ln |u|^2+\frac ...
Jun Lei
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Positive entire solutions of quasilinear elliptic problems via nonsmooth critical point theory [PDF]
Topological Methods in Nonlinear Analysis, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
CONTI, MONICA, GAZZOLA, FILIPPO
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Multiple solutions for nonlinear discontinuous strongly resonant elliptic problems
Abstract and Applied Analysis, 2000 We consider quasilinear strongly resonant problems with discontinuous right-hand side. To develop an existence theory we pass to a multivalued problem by, roughly speaking, filling in the gaps at the discontinuity points.
Nikolaos C. Kourogenis +1 more
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Periodic Solutions of Second-Order Differential Inclusions Systems with -Laplacian
Abstract and Applied Analysis, 2012 The existence of periodic solutions for nonautonomous second-order differential inclusion systems with -Laplacian is considered. We get some existence results of periodic solutions for system, a.e. , , by using nonsmooth critical point theory.
Liang Zhang, Peng Zhang
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Multiple Solutions for a Class of Differential Inclusion System Involving the (p(x),q(x))-Laplacian
Abstract and Applied Analysis, 2012 We consider a differential inclusion system involving the (p(x),q(x))-Laplacian with Dirichlet boundary condition on a bounded domain and obtain two nontrivial solutions under appropriate hypotheses.
Bin Ge, Ji-Hong Shen
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Harnessing Machine Learning to Understand and Design Disordered Solids
Advanced Intelligent Discovery, EarlyView.This review maps the dynamic evolution of machine learning in disordered solids, from structural representations to generative modeling. It explores how deep learning and model explainability transform property prediction into profound physical insight.
Muchen Wang, Yue Fan
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Resonant nonlinear periodic problems with the scalar p-Laplacian and a nonsmooth potential [PDF]
, 2006 We study periodic problems driven by the scalar p-Laplacian with a nonsmooth potential. Using the nonsmooth critical point theory for locally Lipsctiz functions,we prove two existence theorems under conditions of resonance at infinity with respect to ...
Staicu, Vasile +6 more
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Existence and multiplicity for degenerate fractional Kirchhoff problems with nonsmooth potential
Electronic Journal of Qualitative Theory of Differential EquationsThis paper investigates a class of nonlocal variable-order fractional $p(\cdot)$-Kirchhoff type equations with nonsmooth nonlinearities \[ \begin{cases} \mathscr{M}\left(\int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^{p(x,y)}}{p(x,y)|x-y|^{N+s(x,y)p(x,y)}}{\rm
Ziqing Yuan
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