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Complex Variables and Elliptic Equations
An International Journal
Volume 63, 2018 - Issue 9
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Original Articles

Compactness and existence results for an elliptic PDE with zero Dirichlet boundary condition

Obaid AlgahtaniCollege of Sciences, King Saud University, Saudi Arabia.View further author information
,
Hichem ChtiouiFaculté des Sciences de Sfax, Départment de Mathématiques, Université de Sfax, Tunisia.View further author information
,
Ramzi FehemFaculty of Sciences of Tunis, LR03ES04 partial differential equations and applications, University of Tunis El Manar, Tunis, Tunisia.View further author information
&
Hichem HajaiejCalifornia State University, Los Angeles, CA, USA.Correspondence[email protected]
View further author information
Pages 1322-1340 | Received 18 Jul 2017, Accepted 07 Aug 2017, Published online: 09 Oct 2017

References

  • Ambrosetti A , Garcia Azorero J , Peral I . Perturbation of -Δu+u (N+2)/(N-2)=0, the scalar curvature problem in ℝN and related topics. J Funct Anal. 1999;165(1):117–149.
  • Aubin T , Bahri A . Méthodes de topologie algébrique pour le problème de la courbure scalaire prescrite. [Methods of algebraic topology for the problem of prescribed scalar curvature]. J Math Pures Appl. 1997;76(6):525–849. French.
  • Bahri A . An invariant for Yamabe-type flows with applications to scalar curvature problems in high dimensions. A celebration of J. F. Nash Jr., Duke Math J. 1996;81:323–466.
  • Bahri A , Coron JM . The scalar curvature problem on the standard three dimensional spheres. J Funct Anal. 1991;95(1):106–172.
  • Ben Mahmoud R , Chtioui H . Existence results for the prescribed scalar curvature on 𝕊3 . Annales de l’Institut Fourier, (Grenoble). 2011;61(3):971–986.
  • Ben Mahmoud R , Chtioui H . Prescribing the scalar curvature problem on higher-dimensional manifolds. Discrete Contin Dyn Syst. 2012;32(5):1857–1879.
  • Chang SY , Yang P . A perturbation result in prescribing scalar curvature on s n . Duke Math J. 1991;64(1):27–69.
  • Chtioui H , Ben Mahmoud R , Abuzaid DA . Conformal transformation of metrics on the n-sphere. Nonlinear Anal.: TMA. 2013;82:66–81.
  • Chtioui H . Prescribing the scalar curvature problem on three and four manifolds. Adv Nonlinear Stud. 2003;3(4):457–470.
  • Li YY . Prescribing scalar curvature on s n and related topics. Part I, J Differ Equ. 1995;120(2):319–410.
  • Struwe M . Variational methods. Berlin: Springer-Verlag; 1996. (Ergebnisse der Mathematik und ihrer Grenzgebiete; Vol. 34).
  • Struwe M . A global compactness result for elliptic boundary value problem involving limiting nonlinearities. Math Z. 1984;187:511–517.
  • Pohozaev S . Eigenfunctions of the equation Δu+λf(u)=0. Soviet Math Dokl. 1965;6:1408–1411.
  • Bahri A , Coron JM . On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of topology of the domain. Commun Pure Appl Math. 1988;41(3):255–294.
  • Bouchech Z , Chtioui H . Multiplicity and existence results for a nonlinear elliptic equation with Sobolev exponent. Adv Nonlinear Stud. 2010;10:537–572.
  • Sharaf K . A perturbation result for a critical elliptic equation with zero Dirichlet boundary condition. Discrete Contin Dyn Syst. 2017;37:1691–1706.
  • Sharaf K . Positive solutions for a nonlinear problem on a three-dimensional domain. Complex Variable Elliptic Equ. 2017;62:862–875.
  • Sharaf K . Existence of solutions for elliptic nonlinear problems on the unit ball of ℝ3 . Electron J Differ Equ. 2016, Paper No. 229, 9 pp.
  • Sharaf K . On a nonlinear problem with zero Dirichlet boundary condition. Appl Anal. 2017;96:1466–1482.
  • Li YY . Prescribing scalar curvature on s n and related topics. Part II: existence and compactness, Commun Pure Appl Math. 1996;49:541–579.
  • Bahri A . Critical point at infinity in some variational problems. Harlow: Longman Sci. Tech.; 1989. (Pitman research notes in mathematics series; vol. 182).
  • Ben Ayed M , Chen Y , Chtioui H , et al. On the prescribed scalar curvature problem on 4-manifolds. Duke Math J. 1996;84:633–677.
  • Bahri A , Rabinowitz P . Periodic orbits of hamiltonian systems of three body type. Ann Inst H Poincaré Anal Non Linéaire. 1991;8:561–649.

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