Results 21 to 30 of about 2,542,949 (203)
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
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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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Rigidity for general semiconvex entire solutions to the sigma-2 equation [PDF]
arXiv, 2021 We show that every general semiconvex entire solution to the sigma-2 equation is a quadratic polynomial. A decade ago, this result was shown for almost convex solutions.
arxiv
Allen-Cahn equation for the truncated Laplacian: Unusual phenomena
Mathematics in Engineering, 2020 We study entire viscosity solutions of the Allen-Cahn type equation for the truncated Laplacian that are either one dimensional or radial, in order to shed some light on a possible extension of the Gibbons conjecture in this degenerate elliptic setting.
Isabeau Birindelli, Giulio Galise
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Recent rigidity results for graphs with prescribed mean curvature
Mathematics in Engineering, 2021 This survey describes some recent rigidity results obtained by the authors for the prescribed mean curvature problem on graphs u : M → R. Emphasis is put on minimal, CMC and capillary graphs, as well as on graphical solitons for the mean curvature flow ...
Bruno Bianchini +5 more
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Demonstratio Mathematica, 2023 In this article, we investigate the existence and the precise form of finite-order transcendental entire solutions of some system of Fermat-type quadratic binomial and trinomial shift equations in Cn{{\mathbb{C}}}^{n}. Our results are the generalizations
Haldar Goutam, Banerjee Abhijit
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Entire solutions of two certain types of quadratic trinomial q-difference differential equations
AIMS Mathematics, 2023 The main purpose of this paper is to find the explicit forms for entire solutions of two certain types of Fermat-type q-difference differential equations.
Zhenguang Gao, Lingyun Gao , Manli Liu
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New Insights on Keller–Osserman Conditions for Semilinear Systems
MathematicsIn 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
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Positive Radially Symmetric Entire Solutions of p-k-Hessian Equations and Systems
Mathematics, 2022 In this paper, we discuss the existence of positive radially symmetric entire solutions of the p-k-Hessian equation σk1kλDi|Du|p−2Dju=α1k(|x|)f(u), and the general p-k-Hessian system σk1kλDi|Du|p−2Dju=α1k(|x|)f1(v)f2(u), σk1kλDi|Dv|p−2Djv=β1k(|x|)g1(u)g2(
Wei Fan, Limei Dai, Bo Wang
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Entire solutions for a class of variational problems involving the biharmonic operator and Rellich potentials [PDF]
Nolinear Analysis, Vol. 75, No. 9, 2012, 2011 We study existence, multiplicity and qualitative properties of entire solutions for a noncompact problem related to second-order interpolation inequalities with weights.
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