American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 295-304. doi: 10.3934/proc.2003.2003.295

Systems with coupling in $mathbb(R)^N$ class of noncoercive potentials

Marcelo F. Furtado 1, , Liliane A. Maia 2, and  Elves A. B. Silva 2,

1. 

Universidade de Brasília, Departamento de Matemática, 70910-900, Brasília - DF, Brazil
2. 

Departamento de Matemática, UnB, 70910-900 Brasília-DF, Brazil, Brazil

Received  September 2002 Revised  March 2003 Published  April 2003

This paper deals with the existence and multiplicity of solutions to a class of resonant semilinear elliptic system in RN. The main goal is to consider systems with coupling where none of the potentials are coercive. The existence of solution is proved under a critical growth condition on the nonlinearity.
Keywords: Elliptic Systems, Resonant Problems., Nonquadraticity.
Mathematics Subject Classification: 35J50, 35J5.
Citation: Marcelo F. Furtado, Liliane A. Maia, Elves A. B. Silva. Systems with coupling in $mathbb(R)^N$ class of noncoercive potentials. Conference Publications, 2003, 2003 (Special) : 295-304. doi: 10.3934/proc.2003.2003.295
[1]

Fabiana Maria Ferreira, Francisco Odair de Paiva. On a resonant and superlinear elliptic system. Discrete & Continuous Dynamical Systems - A, 2019, 39 (10) : 5775-5784. doi: 10.3934/dcds.2019253
[2]

Yutong Chen, Jiabao Su. Resonant problems for fractional Laplacian. Communications on Pure & Applied Analysis, 2017, 16 (1) : 163-188. doi: 10.3934/cpaa.2017008
[3]

Diego Averna, Nikolaos S. Papageorgiou, Elisabetta Tornatore. Multiple solutions for nonlinear nonhomogeneous resonant coercive problems. Discrete & Continuous Dynamical Systems - S, 2018, 11 (2) : 155-178. doi: 10.3934/dcdss.2018010
[4]

Tan Bui-Thanh, Omar Ghattas. Analysis of the Hessian for inverse scattering problems. Part III: Inverse medium scattering of electromagnetic waves in three dimensions. Inverse Problems & Imaging, 2013, 7 (4) : 1139-1155. doi: 10.3934/ipi.2013.7.1139
[5]

Sari Lasanen. Non-Gaussian statistical inverse problems. Part II: Posterior convergence for approximated unknowns. Inverse Problems & Imaging, 2012, 6 (2) : 267-287. doi: 10.3934/ipi.2012.6.267
[6]

Sari Lasanen. Non-Gaussian statistical inverse problems. Part I: Posterior distributions. Inverse Problems & Imaging, 2012, 6 (2) : 215-266. doi: 10.3934/ipi.2012.6.215
[7]

Tianxiao Wang. Characterizations of equilibrium controls in time inconsistent mean-field stochastic linear quadratic problems. I. Mathematical Control & Related Fields, 2019, 9 (2) : 385-409. doi: 10.3934/mcrf.2019018
[8]

Alexander Krasnosel'skii. Resonant forced oscillations in systems with periodic nonlinearities. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 239-254. doi: 10.3934/dcds.2013.33.239
[9]

Pablo Amster, Mónica Clapp. Periodic solutions of resonant systems with rapidly rotating nonlinearities. Discrete & Continuous Dynamical Systems - A, 2011, 31 (2) : 373-383. doi: 10.3934/dcds.2011.31.373
[10]

Matthias Eller, Daniel Toundykov. Carleman estimates for elliptic boundary value problems with applications to the stablization of hyperbolic systems. Evolution Equations & Control Theory, 2012, 1 (2) : 271-296. doi: 10.3934/eect.2012.1.271
[11]

Antonio Iannizzotto, Nikolaos S. Papageorgiou. Existence and multiplicity results for resonant fractional boundary value problems. Discrete & Continuous Dynamical Systems - S, 2018, 11 (3) : 511-532. doi: 10.3934/dcdss.2018028
[12]

D. Motreanu, V. V. Motreanu, Nikolaos S. Papageorgiou. Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1401-1414. doi: 10.3934/cpaa.2011.10.1401
[13]

G. Bonanno, Salvatore A. Marano. Highly discontinuous elliptic problems. Conference Publications, 1998, 1998 (Special) : 118-123. doi: 10.3934/proc.1998.1998.118
[14]

Wenxiong Chen, Congming Li. Indefinite elliptic problems in a domain. Discrete & Continuous Dynamical Systems - A, 1997, 3 (3) : 333-340. doi: 10.3934/dcds.1997.3.333
[15]

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
[16]

Claudianor O. Alves, Djairo G. De Figueiredo. Nonvariational elliptic systems. Discrete & Continuous Dynamical Systems - A, 2002, 8 (2) : 289-302. doi: 10.3934/dcds.2002.8.289
[17]

Paul H. Rabinowitz. On a class of reversible elliptic systems. Networks & Heterogeneous Media, 2012, 7 (4) : 927-939. doi: 10.3934/nhm.2012.7.927
[18]

Tiphaine Jézéquel, Patrick Bernard, Eric Lombardi. Homoclinic orbits with many loops near a $0^2 i\omega$ resonant fixed point of Hamiltonian systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3153-3225. doi: 10.3934/dcds.2016.36.3153
[19]

Andrés Ávila, Louis Jeanjean. A result on singularly perturbed elliptic problems. Communications on Pure & Applied Analysis, 2005, 4 (2) : 341-356. doi: 10.3934/cpaa.2005.4.341
[20]

Agnese Di Castro, Mayte Pérez-Llanos, José Miguel Urbano. Limits of anisotropic and degenerate elliptic problems. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1217-1229. doi: 10.3934/cpaa.2012.11.1217

 Impact Factor: 

Tools

Metrics

  • PDF downloads (4)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences