American Institute of Mathematical Sciences

Advanced
January  2000, 6(1): 39-50. doi: 10.3934/dcds.2000.6.39

On the existence of multipeak solutions for nonlinear field equations on $R^N$

E. N. Dancer 1, and  Shusen Yan 2,

1. 

School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia
2. 

School of Mathematics and Statistics, University of Sydney, NSW 2006

Received  September 1999 Published  December 1999

In this paper, we construct multipeak solutions with all the peaks close to a designated saddle point or strict local minimum point of the function $Q(y)$ for the nonlinear field equations. We also show that there is no multipeak solution with all its peaks near a strict local maximum point of $Q(y)$.
Keywords: multipeak solution., elliptic problem.
Mathematics Subject Classification: 35B25, 35J6.
Citation: E. N. Dancer, Shusen Yan. On the existence of multipeak solutions for nonlinear field equations on $R^N$. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 39-50. doi: 10.3934/dcds.2000.6.39
[1]

Ling Mi. Asymptotic behavior for the unique positive solution to a singular elliptic problem. Communications on Pure & Applied Analysis, 2015, 14 (3) : 1053-1072. doi: 10.3934/cpaa.2015.14.1053
[2]

Baishun Lai, Qing Luo. Regularity of the extremal solution for a fourth-order elliptic problem with singular nonlinearity. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 227-241. doi: 10.3934/dcds.2011.30.227
[3]

Claudianor Oliveira Alves, Paulo Cesar Carrião, Olímpio Hiroshi Miyagaki. Signed solution for a class of quasilinear elliptic problem with critical growth. Communications on Pure & Applied Analysis, 2002, 1 (4) : 531-545. doi: 10.3934/cpaa.2002.1.531
[4]

Christos V. Nikolopoulos, Georgios E. Zouraris. Numerical solution of a non-local elliptic problem modeling a thermistor with a finite element and a finite volume method. Conference Publications, 2007, 2007 (Special) : 768-778. doi: 10.3934/proc.2007.2007.768
[5]

Juan Dávila, Louis Dupaigne, Marcelo Montenegro. The extremal solution of a boundary reaction problem. Communications on Pure & Applied Analysis, 2008, 7 (4) : 795-817. doi: 10.3934/cpaa.2008.7.795
[6]

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
[7]

Hermann Gross, Sebastian Heidenreich, Mark-Alexander Henn, Markus Bär, Andreas Rathsfeld. Modeling aspects to improve the solution of the inverse problem in scatterometry. Discrete & Continuous Dynamical Systems - S, 2015, 8 (3) : 497-519. doi: 10.3934/dcdss.2015.8.497
[8]

V.N. Malozemov, A.V. Omelchenko. On a discrete optimal control problem with an explicit solution. Journal of Industrial & Management Optimization, 2006, 2 (1) : 55-62. doi: 10.3934/jimo.2006.2.55
[9]

Guillaume Warnault. Regularity of the extremal solution for a biharmonic problem with general nonlinearity. Communications on Pure & Applied Analysis, 2009, 8 (5) : 1709-1723. doi: 10.3934/cpaa.2009.8.1709
[10]

Shaoyong Lai, Yong Hong Wu. The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 401-408. doi: 10.3934/dcdsb.2003.3.401
[11]

Sondes khabthani, Lassaad Elasmi, François Feuillebois. Perturbation solution of the coupled Stokes-Darcy problem. Discrete & Continuous Dynamical Systems - B, 2011, 15 (4) : 971-990. doi: 10.3934/dcdsb.2011.15.971
[12]

Song Wang. Numerical solution of an obstacle problem with interval coefficients. Numerical Algebra, Control & Optimization, 2020, 10 (1) : 23-38. doi: 10.3934/naco.2019030
[13]

Cong Qin, Xinfu Chen. A new weak solution to an optimal stopping problem. Discrete & Continuous Dynamical Systems - B, 2020, 25 (12) : 4823-4837. doi: 10.3934/dcdsb.2020128
[14]

H. M. Yin. Optimal regularity of solution to a degenerate elliptic system arising in electromagnetic fields. Communications on Pure & Applied Analysis, 2002, 1 (1) : 127-134. doi: 10.3934/cpaa.2002.1.127
[15]

E. N. Dancer. Some examples on solution structures for weakly nonlinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (5) : 817-826. doi: 10.3934/dcds.2005.12.817
[16]

Francisco Ortegón Gallego, María Teresa González Montesinos. Existence of a capacity solution to a coupled nonlinear parabolic--elliptic system. Communications on Pure & Applied Analysis, 2007, 6 (1) : 23-42. doi: 10.3934/cpaa.2007.6.23
[17]

Lucio Boccardo, Alessio Porretta. Uniqueness for elliptic problems with Hölder--type dependence on the solution. Communications on Pure & Applied Analysis, 2013, 12 (4) : 1569-1585. doi: 10.3934/cpaa.2013.12.1569
[18]

Galina V. Grishina. On positive solution to a second order elliptic equation with a singular nonlinearity. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1335-1343. doi: 10.3934/cpaa.2010.9.1335
[19]

E. N. Dancer, Danielle Hilhorst, Shusen Yan. Peak solutions for the Dirichlet problem of an elliptic system. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 731-761. doi: 10.3934/dcds.2009.24.731
[20]

Boumediene Abdellaoui, Ahmed Attar. Quasilinear elliptic problem with Hardy potential and singular term. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1363-1380. doi: 10.3934/cpaa.2013.12.1363

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (54)
  • HTML views (0)
  • Cited by (16)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences