Multiple Solutions for an Elliptic Equation with Hardy Potential and Critical Nonlinearity on Compact Riemannian Manifolds

Youssef Maliki, Fatima Zohra Terki

PDF
Journal of Partial Differential Equations ›› 2024, Vol. 37 ›› Issue (1) : 1-24. DOI: 10.4208/jpde.v37.n1.1

Multiple Solutions for an Elliptic Equation with Hardy Potential and Critical Nonlinearity on Compact Riemannian Manifolds

Author information +
History +

Abstract

We prove the existence of multiple solutions of an elliptic equation with critical Sobolev growth and critical Hardy potential on compact Riemannian manifolds.

Keywords

Riemannian manifolds / Yamabe equation / Hardy potential

Cite this article

Download citation ▾
Youssef Maliki, Fatima Zohra Terki. Multiple Solutions for an Elliptic Equation with Hardy Potential and Critical Nonlinearity on Compact Riemannian Manifolds. Journal of Partial Differential Equations, 2024, 37(1): 1‒24 https://doi.org/10.4208/jpde.v37.n1.1

References

[[1]]
Aubin T., Some Nonlinear Analysis Problems in Riemannian Geometry. Springer Monographs in Mathematics, 1998.
[[2]]
Hebey E., Introductionà l’analyse non linéaire sur les variétés. Diderot, 1997.
[[3]]
Madani F., Le problème de Yamabe avec singularités. Bull. Sci. Math., 132 (2008), 5757-591.
[[4]]
Madani F., Le problème de Yamabe avec singularités et la conjecture de Hebey-Vaugon. Thesis, University Pièrre et Marie Curie, 2009.
[[5]]
Aubin T., Problèmes isopérimétriques et espace de Sobolev. Journal of Differenial Geometery, 4 (1976), 573-598.
[[6]]
Talenti G., Best constants in Sobolev inequality. Ann. Mat. Pura Appl., 110 (1976), 353-372.
[[7]]
Caffarelli L. A., Gidas B. and Spruck J., Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth. Comm. Pure Appl. Math., 42 (1989), 271-297.
[[8]]
Hebey E., Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities. Courant lecture notes AMS, 5 (2000).
[[9]]
Terracini S., On positive solutions to a class equations with a singular coefficient and critical exponent. Adv. Diff. Equats., 2 (1996), 241-264.
[[10]]
Ambrosetti A., Malchiodi A., Nonlinear Analysis and Semilinear Elliptic Problems. Cambridge Studies in Advanced Mathematics 104, 2007.
[[11]]
Maliki Y., Terki F. Z., A Struwe type decomposition result for a singular elliptic equation on compcat Riemannian manifold. Anal. Theory Appl., 34 (1) (2018), 17-35.
[[12]]
Benci V., Cerami G. and Passaseo D., On the number of the positive solutions of some nonlinear elliptic problems, in A. Ambrosetti, A. Marino (Eds.), Nonlinear Analysis. A tribute in Honour of Giovanni Prodi. Publ. Sc. Norm. Sup. Pisa, Ed. Norm. Pisa, Pisa, (1991), 93-107.
[[13]]
Benci V., Bonanno C. and Micheletti A. M., On the multilicity of the solutions of non linear elliptic problem on Riemannian manifolds. Journal of Functional Analysis, 252 (2007), 464-489.
[[14]]
Chabrowski J., Yang J., Multiple semiclassical solutions fro the Schrödinger euqation involving a critical exponent. Portugaliae Mathematica, 57 (3) (2000), 273-284.
[[15]]
Terki F. Z., Maliki Y., On the existence of solutions of a critical elliptic equation involving Hardy potential on compact Riemannian manifolds. Note di Matematica, 42 (2) (2022), 19-42.
[[16]]
Druet O., Hebey E. and Robert F., Blow-up Theory for Elliptic PDEs in Riemannian Geometry. Princeton University Press, 2004.
[[17]]
Smet D., Nonlinear Schrödinger equations with Hardy potential and critical nonlinearaties. Transactions of AMS, 357 (7) (2004), 2909-2938.
PDF

Accesses

Citations

Detail

Sections
Recommended

/