Wei‐ming Ni

Wei‐ming Ni's AcademicInfluence.com Rankings

Wei‐ming Ni

Mathematics

#6460

World Rank

#8937

Historical Rank

Measure Theory

#1358

World Rank

#1708

Historical Rank

mathematics Degrees

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Mathematics

Wei‐ming Ni's Degrees

PhD Mathematics Princeton University
Masters Mathematics Princeton University

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Wei‐ming Ni's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Symmetry and related properties via the maximum principle (1979) (2727)
Symmetry of positive solutions of nonlinear elliptic equations in R (1981) (1236)
Large amplitude stationary solutions to a chemotaxis system (1988) (681)
On the shape of least‐energy solutions to a semilinear Neumann problem (1991) (640)
Diffusion, Self-Diffusion and Cross-Diffusion (1996) (614)
Locating the peaks of least energy solutions to a semilinear Neumann problem (1993) (568)
DIFFUSION, CROSS-DIFFUSION, AND THEIR SPIKE-LAYER STEADY STATES (1998) (363)
On the existence of positive entire solutions of a semilinear elliptic equation (1986) (362)
On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems (1995) (318)
DIFFUSION VS CROSS-DIFFUSION : AN ELLIPTIC APPROACH (1999) (281)
Uniqueness and nonuniqueness for positive radial solutions of Δu+f(u,r)=0 (1985) (258)
Singularly Perturbed Elliptic Equations with Symmetry: Existence of Solutions Concentrating on Spheres, Part I (2003) (221)
Global existence, large time behavior and life span of solutions of a semilinear parabolic cauchy problem (1992) (179)
On Conformal Scalar Curvature Equations in Rn (1988) (172)
On the stability and instability of positive steady states of a semilinear heat equation in ℝn (1992) (162)
Turing patterns in the Lengyel-Epstein system for the CIMA reaction (2005) (157)
Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, part II (2004) (151)
Global Dynamics of the Lotka‐Volterra Competition‐Diffusion System: Diffusion and Spatial Heterogeneity I (2016) (150)
Nonexistence theorems for singular solutions of quasilinear partial differential equations (1986) (149)
On the global existence of a cross-diffusion system (1998) (145)
Nonlinear Diffusion Equations and Their Equilibrium States II (1988) (143)
On the asymptotic behavior of solutions of certain quasilinear parabolic equations (1984) (139)
Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents (1992) (133)
On the elliptic equation $\Delta u+Ku^{(n+2)/(n-2)}=0$ and related topics (1985) (131)
Semilinear elliptic equations of Matukuma-type and related topics (1988) (122)
The effects of diffusion and spatial variation in Lotka–Volterra competition–diffusion system I: Heterogeneity vs. homogeneity (2013) (121)
Algorithms and Visualization for solutions of nonlinear Elliptic equations (2000) (119)
Uniqueness of solutions of nonlinear Dirichlet problems (1983) (115)
On the number of interior peak solutions for a singularly perturbed Neumann problem (2007) (115)
Uniqueness and Complete Dynamics in Heterogeneous Competition-Diffusion Systems (2012) (110)
On the Neumann problem for some semilinear elliptic equations and systems of activator-inhibitor type (1986) (109)
On the diffusion coefficient of a semilinear Neumann problem (1988) (107)
Point condensation generated by a reaction-diffusion system in axially symmetric domains (1995) (106)
On the structure of the conformal scalar curvature equation on Rn (1992) (105)
Singular behavior in nonlinear parabolic equations (1985) (102)
Global Bifurcation and Structure of Turing Patterns in the 1-D Lengyel–Epstein Model (2004) (101)
CHAPTER 3 - Qualitative Properties of Solutions to Elliptic Problems (2004) (100)
A counterexample to the nodal domain conjecture and a related semilinear equation (1988) (92)
Global dynamics of the Lotka–Volterra competition–diffusion system with equal amount of total resources, II (2016) (91)
On the elliptic equation Δu+K(x)e2u=0 and conformal metrics with prescribed Gaussian curvatures (1982) (89)
On positive solutions concentrating on spheres for the Gierer–Meinhardt system (2006) (87)
Further study on a nonlinear heat equation (2001) (86)
The effects of diffusion and spatial variation in Lotka–Volterra competition–diffusion system II: The general case (2013) (84)
Carrying capacity in a heterogeneous environment with habitat connectivity. (2017) (72)
On the existence of global vortex rings (1980) (72)
Multiple clustered layer solutions for semilinear Neumann problems on a ball (2005) (69)
On the existence and symmetry properties of finite total mass solutions of the matukuma equation, the eddington equation and their generalizations (1989) (65)
Limiting profiles of semilinear elliptic equations with large advection in population dynamics (2010) (63)
On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem: Intermediate solutions (1998) (63)
Stability of least energy patterns of the shadow system for an activator-inhibitor model (2001) (60)
On the asymptotic behavior and radial symmetry of positive solutions of semilinear elliptic equations in Rn I. Asymptotic behavior (1992) (59)
Perturbations of Second Order Linear Elliptic Problems by Nonlinearities Without Landesman–Lazer Condition (1979) (59)
Dispersal and spatial heterogeneity: single species (2016) (58)
Some Aspects of Semilinear Elliptic Equations on ℝn (1988) (54)
On the asymptotic behavior and radial symmetry of positive solutions of semilinear elliptic equations in Rn II. Radial symmetry (1992) (52)
On $3\times 3$ Lotka-Volterra competition systems with cross-diffusion (1999) (48)
An exterior Dirichlet problem with applications to some nonlinear equations arising in geometry (1984) (47)
The Mathematics of Diffusion (2011) (47)
Effects of dispersal on total biomass in a patchy, heterogeneous system: Analysis and experiment. (2015) (45)
Existence and infinite multiplicity for an inhomogeneous semilinear elliptic equation on ${\bf R}^n$ (2001) (45)
A generalized Pohozaev identity and its applications (1990) (43)
Boundary element monotone iteration scheme for semilinear elliptic partial differential equations (1996) (43)
An introduction to migration-selection pde models (2013) (42)
Traveling fronts of pyramidal shapes in competition-diffusion systems (2013) (42)
On the Stability and Instability of Positive Steady States of a Semilinear Heat Equation in $mathbb{R}^n$ (eng) (1992) (41)
The dynamics of a kinetic activator–inhibitor system (2006) (41)
Some minimax principles and their applications in nonlinear elliptic equations (1980) (41)
On the structure of the conformal Gaussian curvature equation on R2. II (1991) (40)
Pattern formation in a cross-diffusion system (2014) (40)
Global dynamics of the Lotka–Volterra competition–diffusion system with equal amount of total resources, III (2017) (39)
On the structure of the conformal Gaussian curvature equation on $\mathbb{R}^2$ (1991) (39)
On diffusion-induced blowups in a mutualistic model (2001) (38)
On the elliptic equation $Lu - k + K \exp [2u] = 0$ (1985) (36)
Positive solution of fourth order ordinary differential equation with four-point boundary conditions (2006) (36)
On steady states of van der Waals force driven thin film equations (2006) (35)
Monotonicity of stable solutions in shadow systems (2001) (34)
On the positive radial solutions of some semilinear elliptic equations on ℝn (1982) (34)
The existence and stability of nontrivial steady states for S-K-T competition model with cross diffusion (2014) (34)
On the global existence and finite time blow-up of shadow systems (2009) (33)
Mini-ASTROD --- Mini-Astrodynamical Space Test of Relativity using Optical Devices (2003) (31)
An indefinite nonlinear diffusion problem in population gentics,I: Existence and limiting profiles (2010) (31)
Boundary-clustered interfaces for the Allen–Cahn equation (2007) (27)
The Number of Peaks of Positive Solutions of Semilinear Parabolic Equations (1985) (26)
Effects of diffusion on total biomass in heterogeneous continuous and discrete-patch systems (2016) (26)
On Matukuma's equation and related topics (1986) (25)
Dynamics of a consumer–resource reaction–diffusion model (2019) (23)
Effect of Stressors on the Carrying Capacity of Spatially Distributed Metapopulations (2020) (22)
On the rate of convergence and asymptotic profile of solutions to the viscous Burgers equation (2002) (22)
Carrying Capacity of Spatially Distributed Metapopulations. (2020) (19)
Solutions, concentrating on spheres, to symmetric singularly perturbed problems (2002) (18)
A priori estimates of stationary solutions of an activator-inhibitor system (2006) (17)
On the first positive Neumann eigenvalue (2006) (17)
On a singular elliptic equation (1983) (17)
Global dynamics of a general Lotka-Volterra competition-diffusion system in heterogeneous environments (2020) (16)
Advection-mediated competition in general environments (2014) (16)
Recent Progress in Semilinear Elliptic Equations(Solutions for Nonlinear Elliptic Equations) (1989) (15)
Carrying Capacity of a Population Diffusing in a Heterogeneous Environment (2020) (15)
A Note on the Elliptic Sine-Gordon Equation (2003) (14)
Higher Order Approximations in the Heat Equation and the Truncated Moment Problem (2009) (13)
On the effects of carrying capacity and intrinsic growth rate on single and multiple species in spatially heterogeneous environments (2020) (12)
On the Existence and Shape of Solutions to a Semilinear Neumann Problem (1992) (10)
A method to measure the two-dimensional image of magneto-optical Kerr effect (2003) (10)
A new spectrometer using multiple gratings with a two-dimensional charge-coupled diode array detector (2003) (9)
Stability from the point of view of diffusion, relaxation and spatial inhomogeneity (2007) (8)
Diffusion and cross-diffusion in pattern formation (2004) (7)
Algorithms and Visualization for solutions of nonlinear Elliptic equations, Part II: Dirichlet, Neumann and Robin boundary conditions and Problems in 3D (2001) (7)
Nonlinear diffusion equations and their equilibrium states, 3 : proceedings from a conference held August 20-29, 1989 in Gregynog, Wales (1992) (6)
Boundary element monotone iteration scheme for semilinear elliptic partial differential equations, Part II: Quasimonotone iteration for coupled systems (2000) (6)
Directed movement changes coexistence outcomes in heterogeneous environments. (2021) (5)
Periodic solutions for a 3x 3 competitive system with cross-diffusion (2006) (5)
On the least growth of harmonic functions and the boundary behavior of riemann mappings (1985) (4)
Nonlinear diffusion equations and their equilibrium states : proceedings of a microprogram held August 25-September 12, 1986 (1988) (3)
Spike-layers in semilinear elliptic singular Perturbation Problems (1993) (3)
On the existence and boundary behavior of solutions to a class of nonlinear Dirichlet problems (1983) (3)
Some minimax principles with applications in nonlinear elliptic boundary value problems and global vortex flow (1979) (3)
Application of Annular Damper Reaction Wall in Seismic Isolated LNG Tank (2010) (2)
Lane-Emden Equations and Related Topics in Nonlinear Elliptic and Parabolic Problems (1987) (2)
New design of a spectroscopic ellipsometer by using a spectrometer with multiple gratings and a two-dimensional CCD array detector (2004) (2)
Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations (2013) (1)
Dynamics of a periodic-parabolic Lotka–Volterra competition-diffusion system in heterogeneous environments (2022) (1)
2. Dynamics of General Reaction-Diffusion Equations and Systems (2011) (0)
Global dynamics of the Lotka–Volterra competition–diffusion system with equal amount of total resources, III (2017) (0)
EXISTENCE AND NONEXISTENCE OF NONTRIVIAL STEADY STATES OF AN ACTIVATOR-INHIBITOR SYSTEM (Variational Problems and Related Topics) (2008) (0)
On the effects of carrying capacity and intrinsic growth rate on single and multiple species in spatially heterogeneous environments (2020) (0)
Dynamics of a consumer–resource reaction–diffusion model (2019) (0)
THE STUDY OF A AUTO ELLIPSOMETER SYSTEM BY USING A TWO-DIMENSIONAL CCD ARRAY DETECTOR (2003) (0)
5. Beyond Diffusion: Directed Movements, Taxis, and Cross-Diffusion (2011) (0)
1. Introduction: The Heat Equation (2011) (0)
3. Qualitative Properties of Steady States of Reaction-Diffusion Equations and Systems (2011) (0)
Stationary Keller-Segel model with the linear sensitivity(Variational Problems and Related Topics) (1998) (0)
On the behavior of solutions to a semilinear Neumann problem (1987) (0)
4. Diffusion in Heterogeneous Environments: 2 × 2 Lotka–Volterra Competition Systems (2011) (0)
Louis Nirenberg (1925–2020) (2021) (0)
Effects of diffusion on total biomass in heterogeneous continuous and discrete-patch systems (2016) (0)
Global dynamics of the Lotka–Volterra competition–diffusion system with equal amount of total resources, II (2016) (0)
Dispersal and spatial heterogeneity: single species (2015) (0)
Determination of the limit sets of trajectories of the Gierer-Meinhardt system without diffusion (2007) (0)
SOME NONLINEAR EQUATIONS ARISING IN GEOMETRY (2016) (0)
BOUNDARY ELEMENT MONOTONE ITERATION SCHEME (2016) (0)
Gierer-Meinhardt system without diffusion (2018) (0)
CONFORMAL METRICS WITH ZERO SCALAR CURVATURE AND A SYMMETRIZATION PROCESS VIA MAXIMUM PRINCIPLE (1982) (0)

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Wei‐ming Ni's AcademicInfluence.com Rankings