Comptes Rendus
Équations aux dérivées partielles
On the existence of ground state solutions to critical growth problems nonresonant at zero
Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1161-1164.

We prove the existence of ground state solutions to critical growth p-Laplacian and fractional p-Laplacian problems that are nonresonant at zero.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.270
Classification : 35B33, 35J92, 35R11

Kanishka Perera 1

1 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRMATH_2021__359_9_1161_0,
     author = {Kanishka Perera},
     title = {On the existence of ground state solutions to critical growth problems nonresonant at zero},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1161--1164},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {9},
     year = {2021},
     doi = {10.5802/crmath.270},
     language = {en},
}
TY  - JOUR
AU  - Kanishka Perera
TI  - On the existence of ground state solutions to critical growth problems nonresonant at zero
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 1161
EP  - 1164
VL  - 359
IS  - 9
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.270
LA  - en
ID  - CRMATH_2021__359_9_1161_0
ER  - 
%0 Journal Article
%A Kanishka Perera
%T On the existence of ground state solutions to critical growth problems nonresonant at zero
%J Comptes Rendus. Mathématique
%D 2021
%P 1161-1164
%V 359
%N 9
%I Académie des sciences, Paris
%R 10.5802/crmath.270
%G en
%F CRMATH_2021__359_9_1161_0
Kanishka Perera. On the existence of ground state solutions to critical growth problems nonresonant at zero. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1161-1164. doi : 10.5802/crmath.270. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.270/

[1] Gianni Arioli; Filippo Gazzola Some results on p-Laplace equations with a critical growth term, Differ. Integral Equ., Volume 11 (1998) no. 2, pp. 311-326 | MR | Zbl

[2] Zhijie Chen; Naoki Shioji; Wenming Zou Ground state and multiple solutions for a critical exponent problem, NoDEA, Nonlinear Differ. Equ. Appl., Volume 19 (2012) no. 3, pp. 253-277 | DOI | MR

[3] Marco Degiovanni; Sergio Lancelotti Linking solutions for p-Laplace equations with nonlinearity at critical growth, J. Funct. Anal., Volume 256 (2009) no. 11, pp. 3643-3659 | DOI | MR | Zbl

[4] Henrik Egnell Existence and nonexistence results for m-Laplace equations involving critical Sobolev exponents, Arch. Ration. Mech. Anal., Volume 104 (1988) no. 1, pp. 57-77 | DOI | MR | Zbl

[5] Jesús P. Garcia-Azorero; Ireneo Peral Alonso Existence and nonuniqueness for the p-Laplacian: nonlinear eigenvalues, Commun. Partial Differ. Equations, Volume 12 (1987) no. 12, pp. 1389-1430 | MR | Zbl

[6] Mohammed Guedda; Laurent Véron Quasilinear elliptic equations involving critical Sobolev exponents, Nonlinear Anal., Theory Methods Appl., Volume 13 (1989) no. 8, pp. 879-902 | DOI | MR | Zbl

[7] Sunra Mosconi; Kanishka Perera; Marco Squassina; Yang Yang The Brezis–Nirenberg problem for the fractional p-Laplacian, Calc. Var. Partial Differ. Equ., Volume 55 (2016) no. 4, 105, 25 pages | MR | Zbl

[8] Kanishka Perera Nontrivial critical groups in p-Laplacian problems via the Yang index, Topol. Methods Nonlinear Anal., Volume 21 (2003) no. 2, pp. 301-309 | DOI | MR | Zbl

[9] Kanishka Perera; Marco Squassina; Yang Yang Bifurcation and multiplicity results for critical fractional p-Laplacian problems, Math. Nachr., Volume 289 (2016) no. 2-3, pp. 332-342 | DOI | MR | Zbl

[10] Kanishka Perera; Marco Squassina; Yang Yang Bifurcation and multiplicity results for critical p-Laplacian problems, Topol. Methods Nonlinear Anal., Volume 47 (2016) no. 1, pp. 187-194 | MR

[11] Andrzej Szulkin; Tobias Weth; Michel Willem Ground state solutions for a semilinear problem with critical exponent, Differ. Integral Equ., Volume 22 (2009) no. 9-10, pp. 913-926 | MR | Zbl

Cité par Sources :

Commentaires - Politique