Julia Limiting Directions of Entire Solutions of Complex Differential Equations
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DOI: 10.1007/s10473-021-0415-7
Abstract: For entire or meromorphic function f, a value θ ∈ [0, 2π) is called a Julia limiting direction if there is an unbounded sequence {zn} in the Julia set satisfying $$\mathop {\lim }\limits_{n \to \infty… read more here.
Keywords: solutions complex; limiting directions; complex differential; directions entire ... See more keywords
Entire Solutions with Annihilating Fronts to a Nonlocal Dispersal Equation with Bistable Nonlinearity and Spatio-Temporal Delay
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DOI: 10.1007/s10884-015-9450-1
Abstract: This paper deals with the entire solutions to a nonlocal dispersal bistable equation with spatio-temporal delay. Assuming that the equation has a traveling wave front with non-zero wave speed, we establish the existence of entire… read more here.
Keywords: nonlocal dispersal; spatio temporal; temporal delay; equation ... See more keywords
Localized and Expanding Entire Solutions of Reaction–Diffusion Equations
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DOI: 10.1007/s10884-020-09936-2
Abstract: This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction–diffusion equations in $$\mathbb {R}^N$$ R N in any space dimension N . The solutions are assumed to be localized… read more here.
Keywords: reaction diffusion; solutions reaction; entire solutions; diffusion equations ... See more keywords
Entire Solutions of Two Certain Types of Non-linear Differential-Difference Equations
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DOI: 10.1007/s40315-020-00343-8
Abstract: In this paper, we describe entire solutions for two certain types of non-linear differential-difference equations of the form $$\begin{aligned} f^n(z)+\omega f^{n-1}(z)f'(z)+q(z)e^{Q(z)}f(z+c)=u(z)e^{v(z)}, \end{aligned}$$ and $$\begin{aligned} f^n(z)+\omega f^{n-1}(z)f'(z)+q(z)e^{Q(z)}f(z+c)=p_1e^{\lambda z}+p_2e^{-\lambda z}, \end{aligned}$$ where q, Q, u, v are non-constant polynomials, $$c,\lambda… read more here.
Keywords: two certain; solutions two; non linear; types non ... See more keywords
Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation
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DOI: 10.1016/j.jde.2017.03.019
Abstract: Abstract Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin's transformation. The expansions of such singular… read more here.
Keywords: singular radial; solutions prescribed; biharmonic equation; radial entire ... See more keywords
On bounded entire solutions of some quasilinear elliptic equations
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.05.035
Abstract: Abstract In this paper we prove the existence of infinitely many bounded entire solutions, ground state entire solutions and entire solutions with prescribed limit at infinity to PDEs involving the ϕ-Laplace operator in the setting… read more here.
Keywords: bounded entire; elliptic equations; solutions quasilinear; entire solutions ... See more keywords
Entire solutions originating from monotone fronts to the Allen–Cahn equation
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DOI: 10.1016/j.physd.2018.04.003
Abstract: Abstract In this paper, we study entire solutions of the Allen–Cahn equation in one-dimensional Euclidean space. This equation is a scalar reaction–diffusion equation with a bistable nonlinearity. It is well-known that this equation admits three… read more here.
Keywords: originating monotone; cahn equation; solutions originating; allen cahn ... See more keywords
On entire solutions of two types of systems of complex differential-difference equations
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DOI: 10.1016/s0252-9602(16)30124-2
Abstract: Abstract In this paper, we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations, and obtain some interesting results. It extends some results concerning complex differential (difference) equations… read more here.
Keywords: difference equations; differential difference; two types; types systems ... See more keywords
Entire solutions of a variation of the eikonal equation and related PDEs
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DOI: 10.1017/s0013091520000103
Abstract: Abstract 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… read more here.
Keywords: solutions variation; variation eikonal; eikonal equation; equation ... See more keywords
Entire solutions for a delayed nonlocal dispersal system with monostable nonlinearities
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DOI: 10.1088/1361-6544/aaf2e7
Abstract: 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… read more here.
Keywords: system; solutions delayed; dispersal system; delayed nonlocal ... See more keywords
Entire Solutions of the Second-Order Fermat-Type Differential-Difference Equation
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DOI: 10.1155/2020/4871812
Abstract: In this work, we assume that the readers are familiar with general definitions and fundamental theories of Nevanlinna theory [1–3]. f is a meromorphic function which means f is meromorphic in the finite complex plane… read more here.
Keywords: difference; solutions second; second order; order fermat ... See more keywords