Advanced search
Publication Cover
Communications in Partial Differential Equations Volume 22, 1997 - Issue 9-10
Submit an article Journal homepage
341
Views
42
CrossRef citations to date
0
Altmetric
Original Articles

Non—existence of positive solutions to semilinear elliptic equations on r” or r” through the method of moving planes

Bianchi Gabriele Dipartimento di Matematica, Universitá di Ferrara, Via Machiavelli 35, Ferrara, I–44100, Italy
Pages 1671-1690 | Published online: 18 May 2010

Citations (42)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (2)

Jorge García-Melián, Leonelo Iturriaga & Alexander Quaas. (2019) Liouville theorems for radial solutions of semilinear elliptic equations. Complex Variables and Elliptic Equations 64:6, pages 933-949.
Read now
Caifeng Zhang & Zhao Liu. (2016) Liouville-type theorems for integral and PDE systems with critical exponents in a half space. Complex Variables and Elliptic Equations 61:6, pages 731-746.
Read now

Articles from other publishers (40)

Jiaqi Hu & Zhuoran Du. (2023) Nonexistence of anti-symmetric solutions for fractional Hardy–Hénon system. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 154:3, pages 862-886.
Crossref
Qiuping Liao, Zhao Liu & Xinyue Wang. (2024) Liouville type theorems involving fractional order systems. Advanced Nonlinear Studies 24:2, pages 399-414.
Crossref
Francesca Dalbono, Matteo Franca & Andrea Sfecci. (2020) Multiplicity of Radial Ground States for the Scalar Curvature Equation Without Reciprocal Symmetry. Journal of Dynamics and Differential Equations 34:1, pages 701-720.
Crossref
Jing Li & Li Ma. (2022) Moving spheres for semilinear spectral fractional Laplacian equations in the half space. Discrete and Continuous Dynamical Systems 0:0, pages 0-0.
Crossref
Kods Hassine. (2022) Existence and uniqueness of radial solutions for Hardy-Hénon equations involving <i>k</i>-Hessian operators. Communications on Pure and Applied Analysis 21:9, pages 2965.
Crossref
B. Barrios & A. Quaas. (2020) The sharp exponent in the study of the nonlocal Hénon equation in $${\mathbb {R}}^{N}$$: a Liouville theorem and an existence result. Calculus of Variations and Partial Differential Equations 59:4.
Crossref
Francesca Dalbono, Matteo Franca & Andrea Sfecci. (2019) Multiplicity of ground states for the scalar curvature equation. Annali di Matematica Pura ed Applicata (1923 -) 199:1, pages 273-298.
Crossref
M.Á. Burgos-Pérez & J. García-Melián. (2018) Liouville theorems for elliptic systems with nonlinear gradient terms. Journal of Differential Equations 265:12, pages 6316-6351.
Crossref
Matteo Franca & Andrea Sfecci. (2017) Entire Solutions of Superlinear Problems with Indefinite Weights and Hardy Potentials. Journal of Dynamics and Differential Equations 30:3, pages 1081-1118.
Crossref
De Tang. (2016) Positive solutions to semilinear elliptic equations involving a weighted fractional Lapalacian. Mathematical Methods in the Applied Sciences 40:7, pages 2596-2609.
Crossref
Yanyan GUO. (2017) Nonexistence and symmetry of solutions to some fractional laplacian equations in the upper half space. Acta Mathematica Scientia 37:3, pages 836-851.
Crossref
Matteo Franca & Andrea Sfecci. (2017) On a diffusion model with absorption and production. Nonlinear Analysis: Real World Applications 34, pages 41-60.
Crossref
Wei Dai, Zhao Liu & Guozhen Lu. (2016) Liouville Type Theorems for PDE and IE Systems Involving Fractional Laplacian on a Half Space. Potential Analysis 46:3, pages 569-588.
Crossref
Begoña Barrios, Leandro Del Pezzo, Jorge García-Melián & Alexander Quaas. (2017) A Liouville theorem for indefinite fractional diffusion equations and its application to existence of solutions. Discrete & Continuous Dynamical Systems - A 37:11, pages 5731-5746.
Crossref
Cyrill B. Muratov & Xing Zhong. (2017) Threshold phenomena for symmetric-decreasing radial solutions of reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A 37:2, pages 915-944.
Crossref
Wei Dai, Zhao Liu & Guozhen Lu. (2017) Hardy-Sobolev type integral systems with Dirichlet boundary conditions in a half space. Communications on Pure & Applied Analysis 16:4, pages 1253-1264.
Crossref
Florica C. Cîrstea & Frédéric Robert. (2017) Sharp asymptotic profiles for singular solutions to an elliptic equation with a sign‐changing non‐linearity. Proceedings of the London Mathematical Society 114:1, pages 1-34.
Crossref
Xiaohui Yu. (2016) Liouville type theorems for singular integral equations and integral systems. Communications on Pure and Applied Analysis 15:5, pages 1825-1840.
Crossref
Yuxia Guo & Bo Li. (2016) Nonexistence of positive solutions for polyharmonic systems in $\mathbb{R}^N_+$. Communications on Pure and Applied Analysis 15:3, pages 701-713.
Crossref
Isabel Flores & Matteo Franca. (2015) Multiplicity results for the scalar curvature equation. Journal of Differential Equations 259:8, pages 4327-4355.
Crossref
De Tang & Yanqin Fang. (2015) Regularity and nonexistence of solutions for a system involving the fractional Laplacian. Communications on Pure and Applied Analysis 14:6, pages 2431-2451.
Crossref
Alberto Farina. (2015) Symmetry of components, Liouville-type theorems and classification results for some nonlinear elliptic systems. Discrete and Continuous Dynamical Systems 35:12, pages 5869-5877.
Crossref
Jingbo Dou & Ye Li. (2015) Liouville theorem for an integral system on the upper half space. Discrete & Continuous Dynamical Systems - A 35:1, pages 155-171.
Crossref
Yonggang Zhao & Mingxin Wang. (2015) An integral equation involving Bessel potentials on half space. Communications on Pure & Applied Analysis 14:2, pages 527-548.
Crossref
David G. Costa, Olı́mpio H. Miyagaki, Marco Squassina & Jianfu Yang. 2015. Contributions to Nonlinear Elliptic Equations and Systems. Contributions to Nonlinear Elliptic Equations and Systems 133 161 .
Linfen Cao & Wenxiong Chen. (2013) Liouville type theorems for poly-harmonic Navier problems. Discrete & Continuous Dynamical Systems - A 33:9, pages 3937-3955.
Crossref
Xiaohui Yu. (2011) Liouville type theorems for integral equations and integral systems. Calculus of Variations and Partial Differential Equations 46:1-2, pages 75-95.
Crossref
Yanqin Fang & Wenxiong Chen. (2012) A Liouville type theorem for poly-harmonic Dirichlet problems in a half space. Advances in Mathematics 229:5, pages 2835-2867.
Crossref
Yanqin Fang & Jihui Zhang. (2011) Nonexistence of positive solution for an integral equation on a Half-Space $R_+^n$. Communications on Pure and Applied Analysis 12:2, pages 663-678.
Crossref
Matteo Franca. (2010) Positive Solutions for Semilinear Elliptic Equations: Two Simple Models with Several Bifurcations. Journal of Dynamics and Differential Equations 23:3, pages 573-611.
Crossref
Matteo Franca. (2009) Fowler transformation and radial solutions for quasilinear elliptic equations. Part 2: nonlinearities of mixed type. Annali di Matematica Pura ed Applicata 189:1.
Crossref
Athanasios N. Lyberopoulos. (2009) Existence and Liouville-type theorems for some indefinite quasilinear elliptic problems with potentials vanishing at infinity. Journal of Functional Analysis 257:11, pages 3593-3616.
Crossref
Matteo Franca. (2009) Structure Theorems for Positive Radial Solutions of the Generalized Scalar Curvature Equation. Funkcialaj Ekvacioj 52:3, pages 343-369.
Crossref
Wei Min Wang, Li Hong & Kai Tai Li. (2008) Nonexistence of ground states of −Δu = u pp − u q. Acta Mathematica Sinica, English Series 24:5, pages 761-770.
Crossref
E. N. Dancer. (2008) Finite Morse index solutions of supercritical problems. Journal für die reine und angewandte Mathematik (Crelles Journal) 2008:620.
Crossref
. 2007. Superlinear Parabolic Problems. Superlinear Parabolic Problems 377 427 .
YanYan Li & Lei Zhang. (2003) Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations. Journal d'Analyse Mathématique 90:1, pages 27-87.
Crossref
E. Dancer & Yihong Du. (2002) Some remarks on Liouville type results for quasilinear elliptic equations. Proceedings of the American Mathematical Society 131:6, pages 1891-1899.
Crossref
Chang-Shou Lin. (2000) Estimates of the scalar curvature equation via the method of moving planes III. Communications on Pure and Applied Mathematics 53:5, pages 611-646.
Crossref
Meijun Zhu. (2011) Liouville theorems on some indefinite equations. Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129:3, pages 649-661.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.