×
Fan, Linlin; Cao, Linfen; Zhao, Peibiao

Symmetry and monotonicity of positive solutions for Choquard equations involving a generalized tempered fractional \(p\)-Laplacian in \(\mathbb{R}^n\). (English) Zbl 1537.35374

Fract. Calc. Appl. Anal. 26, No. 6, 2757-2773 (2023).

Cited in 1 Document

MSC:

35R11 Fractional partial differential equations
35B06 Symmetries, invariants, etc. in context of PDEs
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J60 Nonlinear elliptic equations
35B09 Positive solutions to PDEs
26A33 Fractional derivatives and integrals

Keywords:

method of moving planes; a generalized tempered fractional \(p\)-Laplacian; radial symmetry; monotonicity
Cite Review PDF
Full Text: DOI

References:

[1] Benci, V.; Micheletti, AM; Visetti, D., An eigenvalue problem for a quasilinear elliptic field equation, J. Differential Equations, 184, 2, 299-320 (2002) · Zbl 1157.35348 · doi:10.1006/jdeq.2001.4155
[2] \(Br \ddot{a}\) ndle, C., Colorado, E., de Pablo, A., \(S \acute{a}\) nchez, U.: A concave-convex elliptic problem involving the fractional Laplacian. Proc. Roy. Soc. Edinburgh Sect. A 143(1), 39-71 (2013) · Zbl 1290.35304
[3] Caffarelli, L.; Silvestre, L., An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations, 32, 7-9, 1245-1260 (2007) · Zbl 1143.26002 · doi:10.1080/03605300600987306
[4] Cao, LF; Fan, LL, Symmetry and monotonicity of positive solutions for a system involving fractional \(p\) &\(q\)-Laplacian in a ball, Complex Var. Elliptic Equ., 68, 4, 667-679 (2023) · Zbl 1510.35369 · doi:10.1080/17476933.2021.2009819
[5] Cao, L.F., Fan, L.L.: Symmetry and monotonicity of positive solutions for a system involving fractional \(p\) &\(q\)-Laplacian in \({\mathbb{R}}^n \). Anal. Math. Phys. 12(2), Paper No. 42 (2022) · Zbl 1485.35377
[6] Cao, LF; Wang, XS, Radial symmetry of positive solutions to a class of fractional Laplacian with a singular nonlinearity, J. Korean Math. Soc., 58, 6, 1449-1460 (2021) · Zbl 1483.35011
[7] Cao, L.F., Wang, X.S., Dai, Z.H.: Radial symmetry and monotonicity of solutions to a system involving fractional \(p\)-Laplacian in a ball. Adv. Math. Phys. 1565731 (2018) · Zbl 1408.35210
[8] Chen, WX; Fang, YQ; Yang, R., Liouville theorems involving the fractional laplacian on a half space, Adv. Math., 274, 167-198 (2015) · Zbl 1372.35332 · doi:10.1016/j.aim.2014.12.013
[9] Chen, WX; Li, CM, Maximum principles for the fractional \(p\)-Laplacian and symmetry of solutions, Adv. Math., 335, 735-758 (2018) · Zbl 1395.35055 · doi:10.1016/j.aim.2018.07.016
[10] Chen, WX; Li, CM; Li, Y., A direct method of moving planes for the fractional Laplacian, Adv. Math., 308, 404-437 (2017) · Zbl 1362.35320 · doi:10.1016/j.aim.2016.11.038
[11] Chen, WX; Li, CM; Ou, B., Qualitative properties of solutions for an integral equation, Discrete Contin. Dyn. Syst., 12, 2, 347-354 (2005) · Zbl 1081.45003 · doi:10.3934/dcds.2005.12.347
[12] Chen, WX; Li, CM; Ou, B., Classification of solutions for an integral equation, Comm. Pure Appl. Math., 59, 3, 330-343 (2006) · Zbl 1093.45001 · doi:10.1002/cpa.20116
[13] Chen, WX; Li, CM; Zhu, JY, Fractional equations with indefinite nonlinearities, Discrete Contin. Dyn. Syst., 39, 3, 1257-1268 (2019) · Zbl 1408.35037 · doi:10.3934/dcds.2019054
[14] Chen, W.X., Wu, L.Y.: A maximum principle on unbounded domains and a liouville theorem for fractional \(p\)-harmonic functions. preprint arXiv: 1905.09986 (2019)
[15] Chen, WX; Zhu, JY, Indefinite fractional elliptic problem and liouville theorems, J. Differential Equations, 260, 5, 4758-4785 (2016) · Zbl 1336.35089 · doi:10.1016/j.jde.2015.11.029
[16] Chen, YG; Liu, BY, Symmetry and non-existence of positive solutions for fractional \(p\)-Laplacian systems, Nonlinear Anal., 183, 303-322 (2019) · Zbl 1415.35276 · doi:10.1016/j.na.2019.02.023
[17] d’Avenia, P.; Siciliano, G.; Squassina, M., On fractional Choquard equations, Math. Models Methods Appl. Sci., 25, 8, 1447-1476 (2015) · Zbl 1323.35205 · doi:10.1142/S0218202515500384
[18] Deng, WH; Li, BY; Tian, WY; Zhang, PW, Boundary problems for the fractional and tempered fractional operators, Multiscale Model. Simul., 16, 1, 125-149 (2018) · Zbl 1391.60104 · doi:10.1137/17M1116222
[19] Fife, PC, Mathematical Aspects of Reacting and Diffusing Systems (1979), Berlin-New York: Springer-Verlag, Berlin-New York · Zbl 0403.92004
[20] Jarohs, S.; Weth, T., Symmetry via antisymmetric maximum principles in nonlocal problems of variable order, Ann. Mat. Pura Appl., 195, 1, 273-291 (2016) · Zbl 1346.35010 · doi:10.1007/s10231-014-0462-y
[21] Le, P., Symmetry of singular solutions for a weighted Choquard equation involving the fractional \(p\)-Laplacian, Commun. Pure Appl. Anal., 19, 1, 527-539 (2020) · Zbl 1423.35403 · doi:10.3934/cpaa.2020026
[22] Le, P., Symmetry of solutions for a fractional \(p\)-Laplacian equation of Choquard type, Internat. J. Math., 31, 4, 2050026 (2020) · Zbl 1477.35300 · doi:10.1142/S0129167X20500263
[23] Le, P., Symmetry of positive solutions to Choquard type equations involving the fractional \(p\)-Laplacian, Acta Appl. Math., 170, 387-398 (2020) · Zbl 1462.35020 · doi:10.1007/s10440-020-00338-6
[24] Ma, LW; Zhang, ZQ, Symmetry of positive solutions for Choquard equations with fractional \(p\)-Laplacian, Nonlinear Anal., 182, 248-262 (2019) · Zbl 1411.35273 · doi:10.1016/j.na.2018.12.015
[25] Marano, SA; Papageorgiou, NS, Constant-sign and nodal solutions of coercive \((p, q)\)-Laplacian problems, Nonlinear Anal., 77, 118-129 (2013) · Zbl 1260.35036 · doi:10.1016/j.na.2012.09.007
[26] Medeiros, E.; Perera, K., Multiplicity of solutions for a quasilinear elliptic problem via the cohomological index, Nonlinear Anal., 71, 9, 3654-3660 (2009) · Zbl 1173.35480 · doi:10.1016/j.na.2009.02.013
[27] Shiri, B.; Wu, GC; Baleanu, D., Collocation methods for terminal value problems of tempered fractional differential equations, Appl. Numer. Math., 156, 385-395 (2020) · Zbl 1455.65238 · doi:10.1016/j.apnum.2020.05.007
[28] Wang, PY; Chen, L.; Niu, PC, Symmetric properties for Choquard equations involving fully nonlinear nonlocal operators, Bull. Braz. Math. Soc. (N.S.), 52, 4, 841-862 (2021) · Zbl 1479.35930 · doi:10.1007/s00574-020-00234-5
[29] Wang, PY; Chen, WX, Hopf’s lemmas for parabolic fractional laplacians and parabolic fractional \(p\)-Laplacians, Commun. Pure Appl. Anal., 21, 9, 3055-3069 (2022) · Zbl 1500.35306 · doi:10.3934/cpaa.2022089
[30] Wang, PY; Dai, ZH; Cao, LF, Radial symmetry and monotonicity for fractional \(H \acute{e}\) non equation in \({\mathbb{R} }^n \), Complex Var. Elliptic Equ., 60, 12, 1685-1695 (2015) · Zbl 1327.35419 · doi:10.1080/17476933.2015.1041937
[31] Wang, XS; Yang, ZD, Symmetry and monotonicity of positive solutions for a Choquard equation with the fractional laplacian, Complex Var. Elliptic Equ., 67, 5, 1211-1228 (2022) · Zbl 1487.35422 · doi:10.1080/17476933.2020.1863385
[32] Zhang, LH; Hou, WW; Ahmad, B.; Wang, GT, Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional \(p\)-Laplacian, Discrete Contin. Dyn. Syst. Ser. S, 14, 10, 3851-3863 (2021) · Zbl 1473.35643
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.