On the existence of ground state solutions to critical growth problems nonresonant at zero

Kanishka Perera

doi:10.5802/crmath.270

Partial differential equations

On the existence of ground state solutions to critical growth problems nonresonant at zero

Kanishka Perera ¹

1. Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA

Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1161-1164.

Abstract

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

Received: 2021-06-23
Accepted: 2021-09-08
Published online: 2021-11-03

DOI: https://doi.org/10.5802/crmath.270
Classification: 35B33, 35J92, 35R11
Author's affiliations:

Kanishka Perera ¹

1. Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA

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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/

References
Cited by

[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 1741848 | Zbl 1131.35325

[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 | Article | MR 2926297

[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 | Article | MR 2514055 | Zbl 1170.35418

[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 | Article | MR 956567 | Zbl 0675.35036

[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 912211 | Zbl 0637.35069

[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 | Article | MR 1009077 | Zbl 0714.35032

[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 3530213 | Zbl 1361.35198

[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 | Article | MR 1998432 | Zbl 1039.47041

[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 | Article | MR 3458311 | Zbl 1336.35050

[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 3469053

[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 2553063 | Zbl 1240.35205

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