American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Fourier-Galerkin method for localized solutions of the Sixth-Order Generalized Boussinesq Equation
  • PROC Home
  • This Issue
  • Next Article
    Synchronized and nonsymmetric phase-locked periodic solutions in a neteork of neurons with McCulloch-Pitts nonlinearity
2001, 2001(Special): 109-120. doi: 10.3934/proc.2001.2001.109

Asymptotic behavior of positive solutions of the equation $ \Delta u + K u^{\frac{n+2}{n-2}} = 0$ in $IR^n$ and positive scalar curvature

Ka Luen Cheung 1, and  Man Chun Leung 2,

1. 

Department of Mathematics, Rutgers University, Hill Center, 110 Frelinghuygen Road, Piscataway, NJ 08854, United States
2. 

Department of Mathematics, National University of Singapore, Singapore 117543, Singapore

Published  November 2013

Please refer to Full Text.
Keywords: positive scalar curvature., Pohozaev's identity, Positive solutions.
Mathematics Subject Classification: Primary: 35J60; Secondary: 58J0.
Citation: Ka Luen Cheung, Man Chun Leung. Asymptotic behavior of positive solutions of the equation $ \Delta u + K u^{\frac{n+2}{n-2}} = 0$ in $IR^n$ and positive scalar curvature. Conference Publications, 2001, 2001 (Special) : 109-120. doi: 10.3934/proc.2001.2001.109
[1]

Alberto Boscaggin, Francesca Colasuonno, Benedetta Noris. Positive radial solutions for the Minkowski-curvature equation with Neumann boundary conditions. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020150
[2]

Yves Coudène, Barbara Schapira. Counterexamples in non-positive curvature. Discrete & Continuous Dynamical Systems - A, 2011, 30 (4) : 1095-1106. doi: 10.3934/dcds.2011.30.1095
[3]

Hiroshi Morishita, Eiji Yanagida, Shoji Yotsutani. Structure of positive radial solutions including singular solutions to Matukuma's equation. Communications on Pure & Applied Analysis, 2005, 4 (4) : 871-888. doi: 10.3934/cpaa.2005.4.871
[4]

Michael E. Filippakis, Nikolaos S. Papageorgiou. Existence and multiplicity of positive solutions for nonlinear boundary value problems driven by the scalar $p$-Laplacian. Communications on Pure & Applied Analysis, 2004, 3 (4) : 729-756. doi: 10.3934/cpaa.2004.3.729
[5]

Wei Long, Shuangjie Peng, Jing Yang. Infinitely many positive and sign-changing solutions for nonlinear fractional scalar field equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 917-939. doi: 10.3934/dcds.2016.36.917
[6]

Leszek Gasiński. Positive solutions for resonant boundary value problems with the scalar p-Laplacian and nonsmooth potential. Discrete & Continuous Dynamical Systems - A, 2007, 17 (1) : 143-158. doi: 10.3934/dcds.2007.17.143
[7]

Shao-Yuan Huang. Exact multiplicity and bifurcation curves of positive solutions of a one-dimensional Minkowski-curvature problem and its application. Communications on Pure & Applied Analysis, 2018, 17 (3) : 1271-1294. doi: 10.3934/cpaa.2018061
[8]

Shao-Yuan Huang. Bifurcation diagrams of positive solutions for one-dimensional Minkowski-curvature problem and its applications. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3443-3462. doi: 10.3934/dcds.2019142
[9]

Ruyun Ma, Man Xu. Connected components of positive solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2701-2718. doi: 10.3934/dcdsb.2018271
[10]

Shao-Yuan Huang. Global bifurcation and exact multiplicity of positive solutions for the one-dimensional Minkowski-curvature problem with sign-changing nonlinearity. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3267-3284. doi: 10.3934/cpaa.2019147
[11]

Mark Pollicott. Closed geodesic distribution for manifolds of non-positive curvature. Discrete & Continuous Dynamical Systems - A, 1996, 2 (2) : 153-161. doi: 10.3934/dcds.1996.2.153
[12]

Huan-Zhen Chen, Zhongxue Lü. Positive solutions to involving Wolff potentials. Communications on Pure & Applied Analysis, 2014, 13 (2) : 773-788. doi: 10.3934/cpaa.2014.13.773
[13]

Meili Li, Maoan Han, Chunhai Kou. The existence of positive periodic solutions of a generalized. Mathematical Biosciences & Engineering, 2008, 5 (4) : 803-812. doi: 10.3934/mbe.2008.5.803
[14]

Alberto Boscaggin, Maurizio Garrione. Positive solutions to indefinite Neumann problems when the weight has positive average. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5231-5244. doi: 10.3934/dcds.2016028
[15]

Yaiza Canzani, Dmitry Jakobson, Igor Wigman. Scalar curvature and $Q$-curvature of random metrics. Electronic Research Announcements, 2010, 17: 43-56. doi: 10.3934/era.2010.17.43
[16]

Marta Strani. Existence and uniqueness of a positive connection for the scalar viscous shallow water system in a bounded interval. Communications on Pure & Applied Analysis, 2014, 13 (4) : 1653-1667. doi: 10.3934/cpaa.2014.13.1653
[17]

Alexei Pokrovskii, Dmitrii Rachinskii. Effect of positive feedback on Devil's staircase input-output relationship. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 1095-1112. doi: 10.3934/dcdss.2013.6.1095
[18]

Jagmohan Tyagi, Ram Baran Verma. Positive solution to extremal Pucci's equations with singular and gradient nonlinearity. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2637-2659. doi: 10.3934/dcds.2019110
[19]

David L. Finn. Noncompact manifolds with constant negative scalar curvature and singular solutions to semihnear elliptic equations. Conference Publications, 1998, 1998 (Special) : 262-275. doi: 10.3934/proc.1998.1998.262
[20]

Haiyan Wang. Existence and nonexistence of positive radial solutions for quasilinear systems. Conference Publications, 2009, 2009 (Special) : 810-817. doi: 10.3934/proc.2009.2009.810

 Impact Factor: 

Tools

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences