Results 31 to 40 of about 10,711,362 (360)

The growth of entire solutions of certain nonlinear differential-difference equations

AIMS Mathematics, 2022
This paper is concerned with entire solutions of nonlinear differential-difference equations. We will characterize the growth of entire solutions for two classes of nonlinear differential-difference equations.
Wenjie Hao, Qingcai Zhang
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LIMITING DIRECTIONS FOR ENTIRE SOLUTIONS OF A

Mathematical reports
Let us consider f as being an entire solution of the differential-difference equation G(z, f)+h(z)fm(z) = 0, (m ∈ N), where h(z) is a transcendental entire function and G(z, f) is a differential-difference polynomial in f with entire coefficients.
Yezhou Li, Zhixue Liu, Heqing Sun
semanticscholar   +1 more source

Entire invariant solutions to Monge-Ampère equations [PDF]

Proceedings of the American Mathematical Society, 2004
We prove existence and regularity of entire solutions to Monge-Ampère equations invariant under an irreducible action of a compact Lie group.
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Uniqueness of entire solutions to quasilinear equations of p-Laplace type

Mathematics in Engineering, 2023
We prove the uniqueness property for a class of entire solutions to the equation $ \begin{equation*} \left\{ \begin{array}{ll} -{\rm div}\, \mathcal{A}(x,\nabla u) = \sigma, \quad u\geq 0 \quad {\text{in }} \mathbb{R}^n, \\ {\liminf\limits_{|x ...
Nguyen Cong Phuc, Igor E. Verbitsky
doaj   +1 more source

Multidimensional entire solutions for an elliptic system modelling phase separation

, 2016
For the system of semilinear elliptic equations \[ \Delta V_i = V_i \sum_{j \neq i} V_j^2, \qquad V_i > 0 \qquad \text{in $\mathbb{R}^N$} \] we devise a new method to construct entire solutions.
Soave, Nicola, Zilio, Alessandro
core   +1 more source

Anisotropic entire large solutions

Comptes Rendus. Mathématique, 2011
Given q∈(0,1], we construct nonradial entire large solutions to the equation Δu=uq in RN.
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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 ...
S. Wu, X. Shen, C. J. Geyer
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Entire solutions of quasilinear elliptic systems on Carnot Groups

, 2013
We prove general a priori estimates of solutions of a class of quasilinear elliptic system on Carnot groups. As a consequence, we obtain several non existence theorems.
D'Ambrosio, Lorenzo, Mitidieri, Enzo
core   +1 more source

New Insights on Keller–Osserman Conditions for Semilinear Systems

Mathematics
In this article, we consider a semilinear elliptic system involving gradient terms of the form Δyx+λ1∇yx=pxfyx,zxifx∈Ω,Δzx+λ2∇zx=qxgyxifx∈Ω, where λ1, λ2∈0,∞, Ω is either a ball of radius R>0 or the entire space RN.
Dragos-Patru Covei
doaj   +1 more source

Generalized Harnack inequality for semilinear elliptic equations

, 2016
This paper is concerned with semilinear equations in divergence form \[ \diver(A(x)Du) = f(u) \] where $f :\R \to [0,\infty)$ is nondecreasing. We prove a sharp Harnack type inequality for nonnegative solutions which is closely connected to the classical
Julin, Vesa
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