Results 31 to 40 of about 1,238 (226)

Degree theory for 4‐dimensional asymptotically conical gradient expanding solitons

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We develop a new degree theory for 4‐dimensional, asymptotically conical gradient expanding solitons. Our theory implies the existence of gradient expanding solitons that are asymptotic to any given cone over S3$S^3$ with non‐negative scalar curvature. We also obtain a similar existence result for cones whose link is diffeomorphic to S3/Γ$S^3/\
Richard H. Bamler, Eric Chen
wiley   +1 more source

On Bounds for Norms of Reparameterized ReLU Artificial Neural Network Parameters: Sums of Fractional Powers of the Lipschitz Norm Control the Network Parameter Vector

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT It is an elementary fact in the scientific literature that the Lipschitz norm of the realization function of a feedforward fully connected rectified linear unit (ReLU) artificial neural network (ANN) can, up to a multiplicative constant, be bounded from above by sums of powers of the norm of the ANN parameter vector.
Arnulf Jentzen, Timo Kröger
wiley   +1 more source

Existence of Solutions of Semilinear Wave Equations With Time‐Dependent Propagation Speed and Time Derivative Nonlinearity

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Consider wave equations with time derivative nonlinearity and time‐dependent propagation speed which are generalized versions of the wave equations in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime, the de Sitter spacetime and the anti‐de Sitter space time.
Kimitoshi Tsutaya, Yuta Wakasugi
wiley   +1 more source

Small but mighty: Impact hazards from iron Near‐Earth Objects

Meteoritics &Planetary Science, EarlyView.
Abstract Small asteroids can impact Earth unexpectedly, as demonstrated by the Chelyabinsk event in 2013. The warning times are likely to be short, and the first tools for fast hazard predictions have been developed in the last years for encounters with rocky or cometary objects, which quickly fragment in the atmosphere and cause airbursts. However, in
Robert Luther, Natalia Artemieva, Andrea Schmalen, Kai Wünnemann, Detlef Koschny, Richard Moissl   +5 more
wiley   +1 more source

The existence of positive solutions for the Neumann problem of p-Laplacian elliptic systems with Sobolev critical exponent

Boundary Value Problems, 2022
The paper aims to consider a class of p-Laplacian elliptic systems with a double Sobolev critical exponent. We obtain the existence result of the above problem under the Neumann boundary for some suitable range of the parameters in the systems.
Bingyu Kou, Tianqing An
doaj   +1 more source

A Variational Formulation for Modeling a Phosphorus Doped Silicon Semiconductor Through a Multi‐Well Approach

Advanced Theory and Simulations, Volume 9, Issue 2, February 2026.
This article develops a variational formulation for modeling a silicon semiconductor through a multiwell approach utilizing phosphorus atoms as a dopant substance. The variational formulation here developed may be used to find an optimal phosphorus density distribution concerning an originally silicon density, in order to maximize the electrical ...
Fabio Silva Botelho
wiley   +1 more source

The Choquard Equation with Weighted Terms and Sobolev-Hardy Exponent

Journal of Function Spaces, 2018
We study a nonlinear Choquard equation with weighted terms and critical Sobolev-Hardy exponent. We apply variational methods and Lusternik-Schnirelmann category to prove the multiple positive solutions for this problem.
Yanbin Sang, Xiaorong Luo, Yongqing Wang
doaj   +1 more source

Multiplicity results for biharmonic equations involving multiple Rellich-type potentials and critical exponents

Boundary Value Problems, 2019
In this paper, a biharmonic equation is investigated, which involves multiple Rellich-type potentials and a critical Sobolev exponent. By using variational methods and analytical techniques, the existence and multiplicity of nontrivial solutions to the ...
Jinguo Zhang, Tsing-San Hsu
doaj   +1 more source

Dimer models and conformal structures

Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 340-446, February 2026.
Abstract Dimer models have been the focus of intense research efforts over the last years. Our paper grew out of an effort to develop new methods to study minimizers or the asymptotic height functions of general dimer models and the geometry of their frozen boundaries.
Kari Astala, Erik Duse, István Prause, Xiao Zhong   +3 more
wiley   +1 more source

Normalized solutions for a fractional coupled critical Hartree system

Electronic Journal of Qualitative Theory of Differential Equations
We consider the existence of normalized solutions for a fractional coupled Hartree system, with the upper critical exponent in the sense of the Hardy-Littelwood-Sobolev inequality.
Shengbing Deng, Wenshan Luo
doaj   +1 more source