带有奇异非线性项的分数阶p-Kirchhoff方程解的存在性问题
Existence of Solutions for a Fractional p-Kirchhoff Equation with Singular Nonlinearity
摘要: 本文主要研究如下带有奇异非线性项的分数阶p-Kirchhoff方程解的存在性:
Abstract: This paper studies the following fractional p-Kirchhoff equation with singular nonlinearity: 
文章引用:张莹. 带有奇异非线性项的分数阶p-Kirchhoff方程解的存在性问题[J]. 理论数学, 2024, 14(4): 137-151. https://doi.org/10.12677/pm.2024.144120

参考文献

[1] Cabré, X. and TanJ. G. (2010) Positive Solutions of Nonlinear Problem Involving the Square Root of the Laplacian. Advances in Mathematics, 224, 2052-2093. [Google Scholar] [CrossRef
[2] Servadei, R. and Valdinoci, E. (2012) Mountain Pass Solutions for Non-Local Elliptic Operators. Journal of Mathematical Analysis and Applications, 389, 887-898. [Google Scholar] [CrossRef
[3] Servadei, R. and Valdinoci, E. (2013) Variational Methods for Non-Local Operators of Elliptic Type. Discrete and Continuous Dynamical Systems, 33, 2105-2137. [Google Scholar] [CrossRef
[4] Daoues, A. and Hammami, A. (2021) Multiplicity Results of a Nonlocal Problem Involving Concave-Convex Nonlinearities. Mathematical Notes, 109, 192-207. [Google Scholar] [CrossRef
[5] Barrios, B., Coloradoc, E., Servadei, R. and Soriaa, F. (2015) A Critical Fractional Equation with Concave-Convex Power Nonlinearities. Annales de I'Institut Henri Poincare, 32, 875-900. [Google Scholar] [CrossRef
[6] Alsulami, H., Kirane, M., Alhodily, S., Saeed, T. and Nyamoradi, N. (2020) Existence and Multiplicity of Solutions to Fractional P-Laplacian Systems with Concave-Convex Nonlinearities. Bulletin of Mathematical Sciences, 10, Article ID: 2050007. [Google Scholar] [CrossRef
[7] Molica Bisci, G. and Servadei, R. (2015) Lower Semicontinuity of Functionals of Fractional Type and Applications to Nonlocal Equations with Critical Sobolev Exponent. Advance in Differential Equations, 20, 635-660. [Google Scholar] [CrossRef
[8] Franzina, G. and Palatucc, G. (2014) Fractional P-Eigenvalues. Rivista di Matematica della Università di Parma, 5, 373-386.
[9] Lindgren, E. and Lindqvist, P. (2013) Fractional Eigenvalues. Calculus of Variations and Partial Differential Equations, 49, 795-826. [Google Scholar] [CrossRef
[10] Razani, A. and Behboudi, F. (2023) Solutions of A (P, Q)-Laplacian Equation Involiving a Super-Linear and a Singular Terms. Ricerche di Matematica, 72, 379-397. [Google Scholar] [CrossRef
[11] Crandall, M.G., Rabinowitz, P.H. and Tartar, L. (1977) On a Dirichlet Problem with a Singular Nonlinearity. Communication in Partial Differential Equations, 2, 193-222. [Google Scholar] [CrossRef
[12] Afrouzi, G.A., Mahdavi, S. and Neghizadeh, Z. (2017) The Nehari Manifold for P-Laplacian Equation with Dirichlet Boundary Condition. Nonlinear Analysis, 12, 143-155. [Google Scholar] [CrossRef
[13] Ben Ali, K., Ghanmi, A. and Kefi, K. (2017) Minimax Method Involving Singular P(X)-Kirchhoff Equation. Journal of Mathematical Physics, 58, Article ID: 111505. [Google Scholar] [CrossRef
[14] Biswas, R. and Tiwari, S. (2020) Nehari Manifold for Fractional P(.)-Laplacian System Involving Concavconvex Nonlinearities. Electronic Journal of Differential Equations, No. 98, 1-29. [Google Scholar] [CrossRef
[15] Ghanmi, A. and Saoudi, K. (2016) The Nehari Manifold for a Singular Elliptic Equation Involving the Fractional Laplace Operator. Fractional Differential Calculus, 6, 201-217. [Google Scholar] [CrossRef
[16] Yang, D.D. and Bai, C.Z. (2020) Multiplicity of Weak Positive Solutions for Fractional p & q Laplacian Problem with Singular Nonlinearity. Journal of Function Spaces, 2020, Article ID: 7424763. [Google Scholar] [CrossRef
[17] Fiscella, A. and Kumar Mishra, P. (2018) The Nehari Manifold for Fractional Kirchhoff Problems Involving Singular and Critical Terms. Nonlinear Analysis, 186, 6-32. [Google Scholar] [CrossRef
[18] Fiscella, A. (2019) A Fractional Kirchhoff Problem Involving a Singular Term and a Critical Nonlinearity. Advances in Nonlinear Analysis, 8, 645-660. [Google Scholar] [CrossRef
[19] Caponi, M. and Pucci, P. (2016) Existence Theorems for Entire Solutions of Stationary Kirchhoff Fractional p-Laplacian Equations. Annali di Matematica Pura ed Applicata, 195, 2099-2129. [Google Scholar] [CrossRef
[20] Zu, S.C. and Suo, H.M. (2022) Multiple Solutions for a Fractional p-Kirchhoff Equation with Critical Growth and Low Order Perturbations. AIMS Mathematics, 7, 12897-12912. [Google Scholar] [CrossRef
[21] Brezis, H. and Mironescu, P. (2001) Composition in Fractional Sobolev Spaces. Discrete & Continuous Dynamical Systems, 7, 241-246. [Google Scholar] [CrossRef
[22] Demengel, F. and Demengel, G. (2012) Functional Spaces for the Theory of Elliptic Partial Differential Equations. Springer, London. [Google Scholar] [CrossRef
[23] DiNezza, E., Palatucci, G. and Valdinoci, E. (2012) Hitchhiker’s Guide to the Fractional Sobolev Spaces. Bulletin des Sciences Mathématiques, 136, 521-573. [Google Scholar] [CrossRef
[24] Drabek, P. BS Pohozaev, S.I. (1997) Positive Solutions for the p-Laplacian: Application of the Fibering Method. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, 127, 703-726. [Google Scholar] [CrossRef
[25] Brezis, H. and Liebesgue, E. (1983) A Relation between Pointwise Convergence of Function and Convergence of Functionals. Proceedings of the American Mathematical Society, 88, 486-490. [Google Scholar] [CrossRef
[26] Wang, X. and Zhang, L. (2019) Existence and Multiplicity of Weak Positive Solutions to a Class of Fractional Laplacian with a Singular Nonlinearity. Results in Mathematics, 74, Article No. 81. [Google Scholar] [CrossRef