Results 31 to 40 of about 13,629,063 (179)
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
doaj +1 more source
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
doaj +1 more source
A nonsmooth critical point theory approach to some nonlinear elliptic equations in {${\Bbb R}^n$}
Differential and Integral Equations, 2000 A quasilinear elliptic equation \[ - \sum^{n}_{i,j=1} D_{j}\bigl(a_{ij}(x,u)D_{i}u\bigr) + \frac 12\sum^{n}_{i,j=1} {\partial a_{ij}\over\partial u} (x,u)D_{i}uD_{j}u + b(x)u = f(x,u) \tag{1} \] in \(\mathbb R^{n}\) is studied. Suppose that \(b\in L^\infty_{\text{loc}} (\mathbb R^{n})\) and \(b\geq b_{0}>0\) almost everywhere for a constant \(b_0 ...
GAZZOLA, FILIPPO, RADULESCU V.
openaire +4 more sources
On a global implicit function theorem for locally Lipschitz maps via non-smooth critical point theory [PDF]
Quaestiones Mathematicae, 2017 We prove a non-smooth generalization of the global implicit function theorem. More precisely we use the non-smooth local implicit function theorem and the non-smooth critical point theory in order to prove a non-smooth global implicit function theorem for locally Lipschitz functions. A comparison between several global inversion theorems is discussed.
Galewski, Marek, Rădulescu, Marius
openaire +3 more sources
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
wiley +1 more source
Periodic solution for second-order impulsive differential inclusions with relativistic operator
Boundary Value Problems, 2018 In this paper, the boundary value problem of a second-order impulsive differential inclusion involving a relativistic operator is studied. First, the singular problem is reduced to an equivalent non-singular problem in order to better apply the ...
Suiming Shang +3 more
doaj +1 more source
Homoclinic solutions for a differential inclusion system involving the p(t)-Laplacian
Advances in Nonlinear Analysis, 2022 The aim of this article is to study nonlinear problem driven by the p(t)p\left(t)-Laplacian with nonsmooth potential. We establish the existence of homoclinic solutions by using variational principle for locally Lipschitz functions and the properties of ...
Cheng Jun, Chen Peng, Zhang Limin
doaj +1 more source
Doubly resonant semilinear elliptic problems via nonsmooth critical point theory
Journal of Differential Equations, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
JEAN NOEL CORVELLEC +2 more
openaire +3 more sources
Topological Aspects of Nonsmooth Optimization [PDF]
, 2011 This book deals with nonsmooth structures arising within the optimization setting. It considers four optimization problems, namely, mathematical programs with complementarity constraints, general semi-infinite programming problems, mathematical programs ...
Shikhman, Vladimir, Vladimir Shikhman
core +1 more source
Advanced Intelligent Discovery, EarlyView.This article outlines how artificial intelligence could reshape the design of next‐generation transistors as traditional scaling reaches its limits. It discusses emerging roles of machine learning across materials selection, device modeling, and fabrication processes, and highlights hierarchical reinforcement learning as a promising framework for ...
Shoubhanik Nath +4 more
wiley +1 more source