拟线性微分方程无限区间上正解的存在性
The Existence of Positive Solutions to Quasilinear Differential Equation on Infinite Intervals
DOI: 10.12677/PM.2023.137217, PDF, 下载: 108  浏览: 142 
作者: 唐旭莹：西北师范大学数学与统计学院，甘肃 兰州
关键词: 不动点定理；拟线性问题；无限区间；正解；Fixed Point Theorem； Quasilinear Problems； Infinite Intervals； Positive Solution
摘要: 运用锥上的不动点定理讨论了无限区间上拟线性问题正解的存在性，其中 K :(0,∞)→(0,∞)和f:[0,∞)× ℝ→[0,∞)连续，N > 2 是整数，R是一个正参数。
Abstract: In this paper, by using the fixed point theorem, we discuss the following quasilinear problems on infinite intervals where K :(0,∞)→(0,∞) and f:[0,∞)× ℝ→[0,∞) are continuous, N > 2 is an integer, R is a positive parameter.
文章引用：唐旭莹. 拟线性微分方程无限区间上正解的存在性[J]. 理论数学, 2023, 13(7): 2103-2110. https://doi.org/10.12677/PM.2023.137217

参考文献

[1] Agarwal, R.P. and O'Regan, D. (2001) Infinite Interval Problems for Differential, Difference and Integral Equations. Kluwer Academic Publishers, Dordrecht.
https://doi.org/10.1007/978-94-010-0718-4 1
[2] Agarwal, R.P., O'Regan, D. and Wong, P.J.Y. (1999) Positive Solutions of Differential, Difference and Integral Equations. Kluwer Academic Publishers, Dordrecht.
https://doi.org/10.1007/978-94-015-9171-3 23
[3] Agarwal, R.P. and O'Regan, D. (2004) An Infinite Interval Problem Arising in Circularly Symmetric Deformations of Shallow Membrane Caps. International Journal of Non-Linear Mechanics, 39, 779-784.
https://doi.org/10.1016/S0020-7462(03)00041-6
[4] Anoop, T.V., Drabek, P. and Sasi, S. (2015) Weighted Quasilinear Eigenvalue Problems in Exterior Domains. Calculus of Variations and Partial Differential Equations, 53, 961-975.
https://doi.org/10.1007/s00526-014-0773-2
[5] Sriskandasingam, M.Y., Sun, S.M. and Zhang, B.Y. (2023) Non-Homogeneous Boundary Value Problems of the Kawahara Equation Posed on a Finite Interval. Nonlinear Analysis, 227, Article 113158.
https://doi.org/10.1016/j.na.2022.113158
[6] Chu, J.F. (2019) On an Infinite-Interval Boundary-Value Problem in Geophysics. Monatshefte fur Mathematik, 188, 621-628.
https://doi.org/10.1007/s00605-017-1153-8
[7] Azeroual, B. and Zertiti, A. (2018) On Multiplicity of Radial Solutions to Dirichlet Problem Involving the p-Laplacian on Exterior Domains. International Journal of Applied Mathematics, 31, 121-147.
https://doi.org/10.12732/ijam.v31i1.9
[8] Chhetri, M. and Drabek, P. (2014) Principal Eigenvalue of p-Laplacian Operator in Exterior Domain. Results in Mathematics, 66, 461-468.
https://doi.org/10.1007/s00025-014-0386-2
[9] Chu, K.D., Hai, D.D. and Shivaji, R. (2019) Uniqueness of Positive Radial Solutions for Infinite Semipositone p-Laplacian Problems in Exterior Domains. Journal of Mathematical Analysis and Applications, 472, 510-525.
https://doi.org/10.1016/j.jmaa.2018.11.037
[10] Crispo, F., Grisanti, C.R. and Maremonti, P. (2016) On the High Regularity of Solutions to the p-Laplacian Boundary Value Problem in Exterior Domains. Annali di Matematica Pura ed Applicata, 195, 821-834.
https://doi.org/10.1007/s10231-015-0491-1
[11] Iaia, J.A. (2017) Existence of Solutions for Semilinear Problems with Prescribed Number of Zeros on Exterior Domains. Journal of Mathematical Analysis and Applications, 446, 591-604.
https://doi.org/10.1016/j.jmaa.2016.08.063
[12] Jiang, Q., Ma, S. and Pasca, D. (2019) Existence and Multiplicity of Solutions for p-Laplacian Neumann Problems. Results in Mathematics, 74, Article No. 67.
https://doi.org/10.1007/s00025-019-0995-x
[13] Li, Y.X. and Wei, M. (2021) Positive Radial Solutions of p-Laplace Equations on Exterior Domains. AIMS Mathematics, 6, 8949-8958.
https://doi.org/10.3934/math.2021519
[14] Son, B.J. and Wang, P.Y. (2022) Positive Radial Solutions to Classes of p-Laplacian Systems on the Exterior of a Ball with Nonlinear Boundary Conditions. Nonlinear Analysis, 2014, Article ID: 4299841.
[15] Jeong, J.M., Kim, C.C. and Lee, K.K. (2019) Existence and Nonexistence of Solutions to p-Laplacian Problems on Unbounded Domains. Mathematics, 7, Article 438.
https://doi.org/10.3390/math7050438
[16] Dai, J. and Zhou, Z.F. (2010) The Existence of Positive Solutions to Boundary Value Problem of Second Order Differential Equations. Annals of Applied Mathematics, 26, 10-15.

为你推荐