带有混合奇异项和测度项的分数阶p-Laplace方程解的存在性问题
Existence of Solutions for Fractional p-Laplacian Problems with Mixed Singular Nonlinearities and Radon Measure
摘要: 本文研究下列带有混合奇异项和测度项的分数阶p-Laplace方程:
Abstract: This paper studies the following fractional p-Laplacian problem with mixed singular nonlinearities and Radon measure:
文章引用:张莹. 带有混合奇异项和测度项的分数阶p-Laplace方程解的存在性问题[J]. 理论数学, 2024, 14(5): 433-446. https://doi.org/10.12677/pm.2024.145198

参考文献

[1] Crandall, M.G., Rabinowitz, P.H. and Tartar, L. (1977) On a Dirichlet Problem with a Singular Nonlinearity. Communications in Partial Differential Equations, 2, 193-222. [Google Scholar] [CrossRef
[2] Coclite, M.M. and Palmieri, G. (1989) On a Singular Nonlinear Dirichlet Problem. Communications in Partial Differential Equations Partial Differential Equations, 14, 1315-1327. [Google Scholar] [CrossRef
[3] Diaz, I.I., Morel, J.M. and Oswald, L. (1987) An Elliptic Equation with Singular Nonlinearity. Communications in Partial Differential Equations Partial Differential Equations, 12, 1333-1344. [Google Scholar] [CrossRef
[4] Ghergu, M. and Rădulescu, V. (2003) Sublinear Singular Elliptic Problems with Two Parameters. Journal of Differential Equations, 195, 520-536. [Google Scholar] [CrossRef
[5] Ghergu, M. and Rădulescu, V. (2005) On a Class of Sublinear Singular Elliptic Problems with Convection Term. Journal of Mathematical Analysis and Applications, 311, 635-646. [Google Scholar] [CrossRef
[6] Boccardo, L. and Orsina, L. (2010) Semilinear Elliptic Equations with Singular Nonlinearities. Calculus of Variations and Partial Differential Equations, 37, 363-380. [Google Scholar] [CrossRef
[7] Barrios, B., De Bonis, I., Medina, M. and Peral, I. (2015) Semilinear Problems for the Fractional Laplacian with a Singular Nonlinearity. Open Mathematics, 13, 390-407. [Google Scholar] [CrossRef
[8] Canino, A., Sciunzi, B. and Trombetta, A. (2016) Existence and Uniqueness for p-Laplace Equations Involving Singular Nonlinearities. Nodea-Nonlinear Differential Equations and Applications, 23, 1-18. [Google Scholar] [CrossRef
[9] Canino, A., Montoro, L., Sciunzi, B. and Squassina, M. (2017) Nonlocal Problems with Singular Nonlinaertiy. Bulletin of Mathematical Biology, 141, 223-250. [Google Scholar] [CrossRef
[10] Masoud, B.A. and Mahmoud, H. (2021) A Fractional Laplacian Problem with Mixed Singular Nonlinearities and Nonregular Data. Journal of Ellipitic and Parabolic Equations, 7, 784-814. [Google Scholar] [CrossRef
[11] Youssfi, A. and Ould Mohmoud, G. (2020) On Singular Equations Involving Fractional Laplacian. Acta Mathematica Scientia, 40, 1289-1315. [Google Scholar] [CrossRef
[12] Demengel, F. and Demengel, G. (2012) Functional Spaces for the Theory of Elliptic Partial Differential Equations. Universitext. Springer, London; EDP Sciences, Les Ulis. [Google Scholar] [CrossRef
[13] Dinezza, E., Palatucci, G. and Valdinoci, E. (2012) Hitchhiker’s Guide to the Fractional Sobolev Spaces. Bulletin of the Malaysian Mathematical Sciences Society, 136, 521-573. [Google Scholar] [CrossRef
[14] Benilan, P., Boccardo L., Gallouet, T., et al. (1995) An L1-Theory of Existence and Uniqueness of Solutions of Nonlinear Elliptic Equations. Annali Della Scuola Normal Superiore Di Pisa-Class Di Scienze, 22, 241-273.
[15] Iannizzotto, A., Mosconi, S. and Squassina, M. (2016) Global Regularity for the Fractional p-Laplacian. Revista Matematica Iberoamericana, 32, 1353-1392. [Google Scholar] [CrossRef