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Entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity [PDF]
Advances in Difference Equations, 2018 This paper is concerned with the existence of entire solutions for a reaction–diffusion equation with doubly degenerate nonlinearity. Here the entire solutions are the classical solutions that exist for all (x,t)∈R2 $(x,t)\in \mathbb{R}^{2}$.
Rui Yan, Xiaocui Li
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Nonradial entire solutions for Liouville systems [PDF]
, 2017 We consider the following system of Liouville equations: $$\left\{\begin{array}{ll}-\Delta u_1=2e^{u_1}+\mu e^{u_2}&\text{in }\mathbb R^2\\-\Delta u_2=\mu e^{u_1}+2e^{u_2}&\text{in }\mathbb R^2\\\int_{\mathbb R^2}e^{u_1}
Battaglia, Luca +2 more
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Entire solutions for the heat equation
Electronic Journal of Differential Equations, 2021 We consider the solutions of the heat equation $$ \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 solutions of Donaldson's equation [PDF]
Pacific Journal of Mathematics, 2010 A serious blunder was found in a previous version of the ...
Weiyong He
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Entire solutions of nonlinear differential-difference equations. [PDF]
Springerplus, 2016 In this paper, we describe the properties of entire solutions of a nonlinear differential-difference equation and a Fermat type equation, and improve several previous theorems greatly. In addition, we also deduce a uniqueness result for an entire function f(z) that shares a set with its shift [Formula: see text], which is a generalization of a result ...
Li C, Lü F, Xu J.
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Entire solutions to semilinear nonlocal equations in $\RR^2$ [PDF]
, 2015 We consider entire solutions to $L u= f(u)$ in $\RR^2$, where $L$ is a general nonlocal operator with kernel $K(y)$. Under certain natural assumtions on the operator $L$, we show that any stable solution is a 1D solution.
Ros-Oton, Xavier, Sire, Yannick
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Large energy entire solutions for the Yamabe equation
Journal of Differential Equations, 2011 The paper under review deals with the construction of finite energy solutions to the Yamabe equation in the whole space \({\mathbb R}^n\). The authors develop an approach which provides examples of non-radial solutions in all dimensions \(n \geq 3\), at the same time providing fine knowledge on the core asymptotic behavior.
Manuel del Pino +3 more
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Entire solutions for some critical equations in the Heisenberg group [PDF]
Opuscula Mathematica, 2022 We complete the study started in the paper [P. Pucci, L.Temperini, On the concentration-compactness principle for Folland-Stein spaces and for fractional horizontal Sobolev spaces, Math. Eng. 5 (2023), Paper no.
Patrizia Pucci, Letizia Temperini
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Negatively Invariant Sets and Entire Solutions [PDF]
Journal of Dynamics and Differential Equations, 2010 Negatively invariant compact sets of autonomous and nonautonomous dynamical systems on a metric space, the latter formulated in terms of processes, are shown to contain a strictly invariant set and hence entire solutions. For completeness the positively invariant case is also considered. Both discrete and continuous time systems are considered.
Kloeden, Peter E., Marín Rubio, Pedro
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Existence and multiplicity results for quasilinear equations in the Heisenberg group [PDF]
Opuscula Mathematica, 2019 In this paper we complete the study started in [Existence of entire solutions for quasilinear equations in the Heisenberg group, Minimax Theory Appl. 4 (2019)] on entire solutions for a quasilinear equation \((\mathcal{E}_{\lambda})\) in \(\mathbb{H}^{n}
Patrizia Pucci
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