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Adaptive regularization using the entire solution surface.
Biometrika, 2009 Several sparseness penalties have been suggested for delivery of good predictive performance in automatic variable selection within the framework of regularization. All assume that the true model is sparse. We propose a penalty, a convex combination of the L1- and L∞-norms, that adapts to a variety of situations including sparseness and nonsparseness ...
Wu S, Shen X, Geyer CJ.
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Entire solutions for the heat equation
Electronic Journal of Differential Equations, 2021 We consider the solutions of the heat equation $$ \partial_t F = \partial_z^2 F $$ which are entire in z and t (caloric functions). We examine the relation of the z-order and z-type of an entire caloric function \(F(t, z)\), viewed as function of z, to its t-order and t-type respectively, if it is viewed as function of \(t\). Also, regarding the zeros \
Vassilis G. Papanicolaou +2 more
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Entire positive solution to the system of nonlinear elliptic equations [PDF]
Boundary Value Problems, 2006 The second-order nonlinear elliptic system −Δu=f1(x)uα+g1(x)u−β+h1(x)uγP(v), −Δv=f2(x)vα+g2(x)v−β+h2(x)vγP(u) with ...
Miaoxin Yao, Lingyun Qiu
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Entire solutions of the spruce budworm model
Advances in Difference Equations, 2018 This paper is concerned with the entire solutions of the spruce budworm model, i.e., solutions defined for all (x,t)∈R2 $(x,t)\in \mathbb{R}^{2}$. Using the comparison argument and sub-super-solution method, three types of the entire solutions are ...
Lina Wang
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Entire solutions of nonhomogenous differential equations
Journal of Mathematical Analysis and Applications, 1991 Entire solutions of nonhomogeneous differential equations of second order with polynomial coefficients in the complex domain are considered and bounds on type and maximum modulus are obtained. Conditions for a solution to be entire and univalent (in the unit circle) are given also: In this well written investigation the author exploits the notion of ...
Salmassi, Mohammad
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SOME ENTIRE SOLUTIONS OF THE ALLEN–CAHN EQUATION
Taiwanese Journal of Mathematics, 2004 The paper deals with entire solutions of a bistable reaction-diffusion equation with Nagumo type nonlinearity, the so called Allen-Cahn equation. The entire solutions are the solutions defined for all \((x,t)\in (\mathbb{R}\times \mathbb{R}).\) The authors show the existence of an entire solution which behaves as two traveling front solutions coming ...
Yoshihisa Morita, Hirokazu Ninomiya
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Radial Symmetry of Entire Solutions of a Biharmonic Equation with Supercritical Exponent
Advanced Nonlinear Studies, 2019 Necessary and sufficient conditions for a regular positive entire solution u of a biharmonic ...
Guo Zongming, Wei Long
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Construction of entire solutions for semilinear parabolic equations
Electronic Journal of Differential Equations, 2008 Entire solutions of parabolic equations (those which are defined for all time) are typically rather rare. For example, the heat equation has exactly one entire solution - the trivial solution.
Michael Robinson
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On the growth of entire solution of a nonlinear differential equation [PDF]
Mathematica Bohemica, 2020 In the paper we consider the growth of entire solution of a nonlinear differential equation and improve some existing results.
Indrajit Lahiri, Shubhashish Das
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The study of solutions for several systems of PDDEs with two complex variables
Demonstratio Mathematica, 2023 The purpose of this article is to describe the properties of the pair of solutions of several systems of Fermat-type partial differential difference equations.
Xu Yi Hui, Liu Xiao Lan, Xu Hong Yan
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