June  2003, 2(2): 171-186. doi: 10.3934/cpaa.2003.2.171

Nonhomogeneous polyharmonic elliptic problems at critical growth with symmetric data

1. 

Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria 04510, Mexico

2. 

Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, 25121, Brescia, Italy

Received  March 2002 Revised  February 2003 Published  June 2003

We show the existence of multiple solutions of a perturbed polyharmonic elliptic problem at critical growth with Dirichlet boundary conditions when the domain and the nonhomogenous term are invariant with respect to some group of symmetries.
Citation: Mónica Clapp, Marco Squassina. Nonhomogeneous polyharmonic elliptic problems at critical growth with symmetric data. Communications on Pure & Applied Analysis, 2003, 2 (2) : 171-186. doi: 10.3934/cpaa.2003.2.171
[1]

Jingbo Dou, Qianqiao Guo. Solutions for polyharmonic elliptic problems with critical nonlinearities in symmetric domains. Communications on Pure & Applied Analysis, 2012, 11 (2) : 453-464. doi: 10.3934/cpaa.2012.11.453

[2]

Peter Poláčik. On the multiplicity of nonnegative solutions with a nontrivial nodal set for elliptic equations on symmetric domains. Discrete & Continuous Dynamical Systems, 2014, 34 (6) : 2657-2667. doi: 10.3934/dcds.2014.34.2657

[3]

Thomas Bartsch, Qianqiao Guo. Multi-bubble nodal solutions to slightly subcritical elliptic problems with Hardy terms in symmetric domains. Discrete & Continuous Dynamical Systems - S, 2021, 14 (6) : 1801-1818. doi: 10.3934/dcdss.2021065

[4]

Leszek Gasiński, Nikolaos S. Papageorgiou. Multiplicity of solutions for Neumann problems with an indefinite and unbounded potential. Communications on Pure & Applied Analysis, 2013, 12 (5) : 1985-1999. doi: 10.3934/cpaa.2013.12.1985

[5]

Teresa D'Aprile. Bubbling solutions for the Liouville equation around a quantized singularity in symmetric domains. Communications on Pure & Applied Analysis, 2021, 20 (1) : 159-191. doi: 10.3934/cpaa.2020262

[6]

Yuxin Ge, Ruihua Jing, Feng Zhou. Bubble tower solutions of slightly supercritical elliptic equations and application in symmetric domains. Discrete & Continuous Dynamical Systems, 2007, 17 (4) : 751-770. doi: 10.3934/dcds.2007.17.751

[7]

Christine Chambers, Nassif Ghoussoub. Deformation from symmetry and multiplicity of solutions in non-homogeneous problems. Discrete & Continuous Dynamical Systems, 2002, 8 (1) : 267-281. doi: 10.3934/dcds.2002.8.267

[8]

Junping Shi, Ratnasingham Shivaji. Exact multiplicity of solutions for classes of semipositone problems with concave-convex nonlinearity. Discrete & Continuous Dynamical Systems, 2001, 7 (3) : 559-571. doi: 10.3934/dcds.2001.7.559

[9]

Jiafeng Liao, Peng Zhang, Jiu Liu, Chunlei Tang. Existence and multiplicity of positive solutions for a class of Kirchhoff type problems at resonance. Discrete & Continuous Dynamical Systems - S, 2016, 9 (6) : 1959-1974. doi: 10.3934/dcdss.2016080

[10]

Inara Yermachenko, Felix Sadyrbaev. Types of solutions and multiplicity results for second order nonlinear boundary value problems. Conference Publications, 2007, 2007 (Special) : 1061-1069. doi: 10.3934/proc.2007.2007.1061

[11]

Masataka Shibata. Multiplicity of positive solutions to semi-linear elliptic problems on metric graphs. Communications on Pure & Applied Analysis, 2021, 20 (12) : 4107-4126. doi: 10.3934/cpaa.2021147

[12]

Jaime Arango, Adriana Gómez. Critical points of solutions to elliptic problems in planar domains. Communications on Pure & Applied Analysis, 2011, 10 (1) : 327-338. doi: 10.3934/cpaa.2011.10.327

[13]

Monica Lazzo, Paul G. Schmidt. Nodal properties of radial solutions for a class of polyharmonic equations. Conference Publications, 2007, 2007 (Special) : 634-643. doi: 10.3934/proc.2007.2007.634

[14]

Dušan D. Repovš. Infinitely many symmetric solutions for anisotropic problems driven by nonhomogeneous operators. Discrete & Continuous Dynamical Systems - S, 2019, 12 (2) : 401-411. doi: 10.3934/dcdss.2019026

[15]

Giorgio Fusco, Francesco Leonetti, Cristina Pignotti. On the asymptotic behavior of symmetric solutions of the Allen-Cahn equation in unbounded domains in $\mathbb{R}^2$. Discrete & Continuous Dynamical Systems, 2017, 37 (2) : 725-742. doi: 10.3934/dcds.2017030

[16]

Craig Cowan, Pierpaolo Esposito, Nassif Ghoussoub. Regularity of extremal solutions in fourth order nonlinear eigenvalue problems on general domains. Discrete & Continuous Dynamical Systems, 2010, 28 (3) : 1033-1050. doi: 10.3934/dcds.2010.28.1033

[17]

Joseph Iaia. Existence of infinitely many solutions for semilinear problems on exterior domains. Communications on Pure & Applied Analysis, 2020, 19 (9) : 4269-4284. doi: 10.3934/cpaa.2020193

[18]

Riccardo Molle, Donato Passaseo. On the behaviour of the solutions for a class of nonlinear elliptic problems in exterior domains. Discrete & Continuous Dynamical Systems, 1998, 4 (3) : 445-454. doi: 10.3934/dcds.1998.4.445

[19]

Rubén Figueroa, Rodrigo López Pouso, Jorge Rodríguez–López. Existence and multiplicity results for second-order discontinuous problems via non-ordered lower and upper solutions. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 617-633. doi: 10.3934/dcdsb.2019257

[20]

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

2020 Impact Factor: 1.916

Metrics

  • PDF downloads (45)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]