American Institute of Mathematical Sciences

Advanced
February  2004, 10(1&2): 507-515. doi: 10.3934/dcds.2004.10.507

A new variational characterization of spatially heteroclinic solutions of a semilinear elliptic PDE

Paul H. Rabinowitz 1,

1. 

Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706, United States

Received  June 2002 Revised  March 2003 Published  October 2003

This paper provides a new variational characterization of a spatially heteroclinic solution for a family of semilinear elliptic PDE's.
Keywords: renormalized functional., spatially heteroclinic solution, semilinear elliptic PDE, minimization methods.
Mathematics Subject Classification: 35J20, 35J60, 58E1.
Citation: Paul H. Rabinowitz. A new variational characterization of spatially heteroclinic solutions of a semilinear elliptic PDE. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 507-515. doi: 10.3934/dcds.2004.10.507
[1]

Diane Denny. A unique positive solution to a system of semilinear elliptic equations. Conference Publications, 2013, 2013 (special) : 193-195. doi: 10.3934/proc.2013.2013.193
[2]

Wolf-Jüergen Beyn, Janosch Rieger. Galerkin finite element methods for semilinear elliptic differential inclusions. Discrete and Continuous Dynamical Systems - B, 2013, 18 (2) : 295-312. doi: 10.3934/dcdsb.2013.18.295
[3]

Hongwei Lou, Xueyuan Yin. Minimization of the elliptic higher eigenvalues for multiphase anisotropic conductors. Mathematical Control and Related Fields, 2018, 8 (3&4) : 855-877. doi: 10.3934/mcrf.2018038
[4]

Chady Ghnatios, Guangtao Xu, Adrien Leygue, Michel Visonneau, Francisco Chinesta, Alain Cimetiere. On the space separated representation when addressing the solution of PDE in complex domains. Discrete and Continuous Dynamical Systems - S, 2016, 9 (2) : 475-500. doi: 10.3934/dcdss.2016008
[5]

Yimei Li, Jiguang Bao. Semilinear elliptic system with boundary singularity. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2189-2212. doi: 10.3934/dcds.2020111
[6]

Rafael Ortega, James R. Ward Jr. A semilinear elliptic system with vanishing nonlinearities. Conference Publications, 2003, 2003 (Special) : 688-693. doi: 10.3934/proc.2003.2003.688
[7]

Lei Wei, Zhaosheng Feng. Isolated singularity for semilinear elliptic equations. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 3239-3252. doi: 10.3934/dcds.2015.35.3239
[8]

Olesya V. Solonukha. On nonlinear and quasiliniear elliptic functional differential equations. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 869-893. doi: 10.3934/dcdss.2016033
[9]

Takashi Kajiwara. A Heteroclinic Solution to a Variational Problem Corresponding to FitzHugh-Nagumo type Reaction-Diffusion System with Heterogeneity. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2133-2156. doi: 10.3934/cpaa.2017106
[10]

Gabrielle Nornberg, Delia Schiera, Boyan Sirakov. A priori estimates and multiplicity for systems of elliptic PDE with natural gradient growth. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3857-3881. doi: 10.3934/dcds.2020128
[11]

Xavier Cabré. Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 425-457. doi: 10.3934/dcds.2008.20.425
[12]

Robert Jensen, Andrzej Świech. Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE. Communications on Pure and Applied Analysis, 2005, 4 (1) : 199-207. doi: 10.3934/cpaa.2005.4.187
[13]

Tomás Caraballo, María J. Garrido–Atienza, Björn Schmalfuss, José Valero. Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 439-455. doi: 10.3934/dcdsb.2010.14.439
[14]

Burcu Gürbüz. A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021069
[15]

Defei Zhang, Ping He. Functional solution about stochastic differential equation driven by $G$-Brownian motion. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 281-293. doi: 10.3934/dcdsb.2015.20.281
[16]

Sanming Liu, Zhijie Wang, Chongyang Liu. On convergence analysis of dual proximal-gradient methods with approximate gradient for a class of nonsmooth convex minimization problems. Journal of Industrial and Management Optimization, 2016, 12 (1) : 389-402. doi: 10.3934/jimo.2016.12.389
[17]

Andrea Malchiodi. Topological methods for an elliptic equation with exponential nonlinearities. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 277-294. doi: 10.3934/dcds.2008.21.277
[18]

Dongho Chae. Existence of a semilinear elliptic system with exponential nonlinearities. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 709-718. doi: 10.3934/dcds.2007.18.709
[19]

Junping Shi, R. Shivaji. Semilinear elliptic equations with generalized cubic nonlinearities. Conference Publications, 2005, 2005 (Special) : 798-805. doi: 10.3934/proc.2005.2005.798
[20]

Xavier Cabré, Manel Sanchón, Joel Spruck. A priori estimates for semistable solutions of semilinear elliptic equations. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 601-609. doi: 10.3934/dcds.2016.36.601

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (61)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy