Results 301 to 310 of about 10,711,362 (360)

Entire solutions of certain type of non-linear differential equations

Mathematica Slovaca, 2020
Utilizing Nevanlinna’s value distribution theory of meromorphic functions, we study transcendental entire solutions of the following type nonlinear differential equations in the complex plane f n ( z ) + P ( z , f , f ′ , … , f ( t ) ) = P 1 e α 1 z + P ...
Boqing Xue
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Entire Solutions of Discrete Elliptic Equations

Southeast Asian Bulletin of Mathematics, 2003
By means of monotone methods, comparison theorems for the existence and uniqueness of solutions of discrete elliptic type partial difference equations are derived. The results permit to find positive and bounded solutions to several specific equations.
Pao, C. V., Cheng, S. S.
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Entire solutions of differential equations with finite order transcendental entire coefficients

Acta Mathematica Sinica, 1997
The authors consider the nonhomogeneous linear differential equation \(f^{(k)}+ A_{k-1}f^{(k-1)}+\cdots +A_0f=F\). Here, they use Nevanlinna's value distribution theory to investigate the complex oscillation of this system when the coefficients and the nonhomogeneous function \(F\) are transcendental entire functions of finite order, such that there ...
Chen, Zongxuan, Gao, Shian
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Entire solutions of the Monge‐Ampère equation

Communications on Pure and Applied Mathematics, 1996
It is shown that the Monge-Ampère equation \(\text{det } D^2 u= f\), where \(f\) is pinched between two positive constants, has infinitely many genuinely distinct solutions in the whole Euclidean space.
Chou, Kai-Seng, Wang, Xu-Jia
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Entire solutions of a variation of the eikonal equation and related PDEs

Proceedings of the Edinburgh Mathematical Society, 2020
The aim of this paper is twofold. The first aim is to describe the entire solutions of the partial differential equation (PDE) $u_{z_1}^2+2Bu_{z_1}u_{z_2}+u_{z_2}^2=e^g$, where B is a constant and g is a polynomial or an entire function in $\mathbb {C}^2$
F. Lü
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Localized and Expanding Entire Solutions of Reaction–Diffusion Equations

Journal of Dynamics and Differential Equations, 2020
This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction–diffusion equations in $$\mathbb {R}^N$$ R N in any space dimension N . The solutions are assumed to be localized in the past.
François Hamel, Hirokazu Ninomiya
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Entire Solutions to a Lattice Fisher-KPP System

Discrete and Continuous Dynamical Systems - B, 2023
The authors study the following lattice system of Fisher-KPP type (with Dirichlet boundary condition at \(n=0\)): \[ u'_n(t)=u_{n+1}(t)-2u_n(t)+u_{n-1}(t)+f(u_n(t)), \quad n\in \mathbb{Z}. \] They first establish the existence of a unique positive stationary solution \(\{u_n\}\) and show its stability. Then they construct two types of entire solutions,
Cheng, Cui-Ping, Lou, Bendong, Suo, Jinzhe   +2 more
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Entire solutions of the KPP equation

Communications on Pure and Applied Mathematics, 1999
The paper deals with the solutions defined for all time of the KPP equation \[ u_t=u_{xx}+f(u ...
Hamel, F., Nadirashvili, N.
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Entire solutions for a delayed nonlocal dispersal system with monostable nonlinearities

Nonlinearity, 2019
The paper is concerned with the existence and qualitative properties of entire solutions for a delayed nonlocal dispersal system with monostable nonlinearities. We first prove the existence of traveling wave fronts and a spatially independent solution of
Yanling Meng, Zhixian Yu, Cheng-Hsiung Hsu   +2 more
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Entire solutions of delayed reaction‐diffusion equations

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2011
AbstractThis paper is concerned with entire solutions of delayed reaction‐diffusion equations. Using the comparing argument and sub‐super solutions method, we obtain the existence of entire solutions which behave as two wave fronts coming from the both sides of x‐axis, where an entire solution is meant by a classical solution defined for all space and ...
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