Results 51 to 60 of about 2,542,949 (203)
Existence of entire positive solutions for a class of semilinear elliptic systems
Electronic Journal of Differential Equations, 2010 Under simple conditions on $f_i$ and $g_i$, we show the existence of entire positive radial solutions for the semilinear elliptic system $$displaylines{ Delta u =p(|x|)f_1(v)f_2(u)cr Delta v =q(|x|)g_1(v)g_2(u), }$$ where $xin mathbb{R}^N$, $Ngeq ...
Zhijun Zhang
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Existence and stability properties of entire solutions to the polyharmonic equation $(-Δ)^m u=e^u$ for any $m\ge 1$ [PDF]
arXiv, 2014 We study existence and stability properties of entire solutions of a polyharmonic equation with an exponential nonlinearity. We study existence of radial entire solutions and we provide some asymptotic estimates on their behavior at infinity. As a first result on stability we prove that stable solutions (not necessarily radial) in dimensions lower than
arxiv
The exact entire solutions of certain type of nonlinear difference equations [PDF]
arXiv, 2020 In this paper, we consider the entire solutions of nonlinear difference equation $$f^3+q(z)\Delta f=p_1 e^{\alpha_1 z}+ p_2 e^{\alpha_2 z} $$ where $q$ is a polynomial, and $p_1, p_2, \alpha_1, \alpha_2$ are nonzero constants with $\alpha_1\neq \alpha_2$. It is showed that if $f$ is a non-constant entire solution of $\rho_2(f)<1$ to the above equation,
arxiv
Existence for (p, q) critical systems in the Heisenberg group
Advances in Nonlinear Analysis, 2019 This paper deals with the existence of entire nontrivial solutions for critical quasilinear systems (𝓢) in the Heisenberg group ℍn, driven by general (p, q) elliptic operators of Marcellini types.
Pucci Patrizia, Temperini Letizia
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Entire solutions to semilinear nonlocal equations in $\RR^2$
, 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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Demonstratio MathematicaThis study is devoted to exploring the existence and the precise form of finite-order transcendental entire solutions of second-order trinomial partial differential-difference equations L(f)2+2hL(f)f(z1+c1,z2+c2)+f(z1+c1,z2+c2)2=eg(z1,z2)L{(f)}^{2}+2hL(f)
Xu Hong Yan, Haldar Goutam
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Entire solutions for nonlinear differential-difference equations
Electronic Journal of Differential Equations, 2015 In this article, we study entire solutions of the nonlinear differential-difference equation $$ q(z)f^{n}(z)+a(z)f^{(k)}(z+1)=p_1(z)e^{q_1(z)}+p_2(z)e^{q_2(z)} $$ where $p_1(z)$, $p_2(z)$ are nonzero polynomials, $q_1(z)$, $q_2(z)$ are ...
Na Xu, Ting-Bin Cao, Kai Liu
doaj
Entire solutions originating from three fronts to a two-dimensional nonlocal periodic lattice dynamical system [PDF]
arXiv, 2019 This paper is concerned with the entire solutions of a two-dimensional nonlocal periodic lattice dynamical system. With bistable assumption, it is well known that the system has three different types of traveling fronts. The existence of merging-front entire solutions originating from two fronts for the system have been established by Dong, Li \& Zhang
arxiv
Entire Solutions of the Second-Order Fermat-Type Differential-Difference Equation
Journal of Mathematics, 2020 In this paper, the entire solutions of finite order of the Fermat-type differential-difference equation f″z2+△ckfz2=1 and the system of equations f1″z2+△ckf2z2=1 and f2″z2+△ckf1z2=1 have been studied.
Guoqiang Dang, Jinhua Cai
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Entire holomorphic curves on a Fermat surface of low degree [PDF]
arXiv, 2016 The purpose of the paper is to study some problems raised by Hayman and Gundersen about the existence of non-trivial entire and meromorphic solutions for the Fermat type functional equation $f^n+g^n+h^n=1$. Hayman showed that no non-trivial meromorphic solutions and entire solutions exist when $n \ge 9$ and $n \ge 7$ respectively.
arxiv