具有多个参数的分数p-Laplace边值问题多解的存在性
The Existence of Multiple Solutions for the Valued p-Laplace Boundary Problem with Multiple Parameters
摘要: 分数阶微分方程是微分方程中重要的研究对象。带有p-Laplace算子的分数阶微分方程是分数阶微分方程的推广，也是一类重要的函数问题，因此研究带有p-Laplace算子的分数阶微分方程具有一定意义。对于分数阶p-Laplace微分方程解的存在性的研究已经相对比较成熟，但对于本文这类具有多个参数的分数p-Laplace边值问题的研究相对较少。本文使用临界点定理得到这类具有多个参数的分数p-Laplace微分方程的三个解的存在性。
Abstract: The research of the subordinate order differential is an important figure in the object division. The fractional differential equation with p-Laplace operator is an extension of the fractional differential equation, and it is also an important problem. Therefore, it is meaningful to study the fractional differential equation with p-Laplace operator. The research on the existence of solutions of fractional p-Laplace differential equations has been relatively mature, but there are relatively few researches on fractional p-Laplace boundary value problems with multiple parameters in this paper. In this paper, the critical point theorem is used to obtain the existence of three solutions of this type of fractional p-Laplace differential equation with multiple parameters.
文章引用：章越, 田玉. 具有多个参数的分数p-Laplace边值问题多解的存在性[J]. 理论数学, 2021, 11(11): 1923-1932. https://doi.org/10.12677/PM.2021.1111215

参考文献

[1] Bai, Z.B., Sun, S.J., Du, Z.J., et al. (2020) The Green Function for a Class of Caputo Fractional Differential Equations with a Convection Term. Fractional Calculus and Applied Analysis, 23, 787-798. [Google Scholar] [CrossRef] 
[2] Tian, Y.S., Bai, Z.B. and Sun, S.J. (2019) Positive Solutions for a Boundary Value Problem of Fractional Differential Equation with p-Laplacian Operator. Advances in Difference Equa-tions, 2019, Article No. 349. [Google Scholar] [CrossRef] 
[3] Bai, Z.B., Cheng, Y. and Sun, S.J. (2020) On solutions of a Class of Three-Point Fractional Boundary Value Problems. Boundary Value Problems, 2020, 3063-3073. [Google Scholar] [CrossRef] 
[4] Yue, Y., Tian, Y. and Bai, Z.B. (2019) Infinitely Many Nonnegative Solutions for a Fractional Differential Inclusion with Oscillatory Potential. Applied Mathematics Letters, 88, 64-72. [Google Scholar] [CrossRef] 
[5] Jia, M., Li, L., Liu, X.P., et al. (2019) A Class of Nonlocal Problems of Fractional Differential Equations with Composition of Derivative and Parameters. Advances in Difference Equations, 2019, Article No. 280. [Google Scholar] [CrossRef] 
[6] Wang, S.Q. and Bai, Z.B. (2020) Existence and Uniqueness of Solutions for a Mixed p-Laplace Boundary Value Problem Involving Fractional Derivatives. Advances in Difference Equations, 2020, Article No. 694. [Google Scholar] [CrossRef] 
[7] Kamache, F., Guefaifia, R. and Boulaaras, S. (2020) Existence of Three Solutions for Perturbed Nonlinear Fractional p-Laplacian Boundary Value Systems with Two Control Parameters. Journal of Pseudo-Differential Operators and Applications, 11, Article No. 131. [Google Scholar] [CrossRef] 
[8] Kamache, F., Guefaifia, R., Boulaaras, S., et al. (2020) Existence of Weak Solutions for a New Class of Fractional p-Laplacian Boundary Value Systems. Mathematics, 8, 475. [Google Scholar] [CrossRef] 
[9] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., et al. (2006) The-ory and Applications of Fractional Differential Equations. Elsevier Science, Amsterdam. [Google Scholar] [CrossRef] 
[10] Jiao, F. and Zhou, Y. (2012) Existence Results for Frac-tional Boundary Value Problem via Critical Point Theory. International Journal of Bifurcation & Chaos, 22, 368-224. [Google Scholar] [CrossRef] 
[11] Li, D., Chen, F. and An, Y. (2018) Existence and Multiplicity of Nontrivial Solutions for Nonlinear Fractional Differential Systems with p-Laplacian via Critical Point Theory. Mathematical Methods in the Applied Sciences, 41, 3197-3212. [Google Scholar] [CrossRef] 
[12] Zhou, Y., Wang, J.R. and Zhang, L. (2017) Basic Theory of Fractional Differential Equations: Second Edition. World Scientific Publishing Co. Pte. Ltd., Hackensack. [Google Scholar] [CrossRef] 
[13] Zhou, Y. (2016) Basic Theory of Frac-tional Differential Equations. Springer, Cham. [Google Scholar] [CrossRef] 
[14] Zeidler, E. (1985) Nonlinear Functional Analysis and Its Applications. Volume II, Springer, Berlin.
[15] Ricceri, B. (2009) A Further Three Critical Points Theorem. Nonlinear Analysis, 71, 4151-4157. [Google Scholar] [CrossRef] 
[16] Mei, J. and Liu, X. (2014) Multiplicity of Solutions for Integral Boundary Value Problems of Fractional Differential Equations with Upper and Lower Solutions. Applied Mathematics and Computation, 232, 313-323. [Google Scholar] [CrossRef] 

为你推荐