RINCON M A, LIU I S, HUARCAYA W R, et al. Numerical Analysis for a Nonlinear Model of Elastic Strings with Moving Ends [J]. Applied Numerical Mathematics, 2019, 135: 146-164. doi: 10.1016/j.apnum.2018.08.014
KIRCHHOFF G R. Vorlesungen Vber Matematische Physik: Mechbanlik [M]. Leipzig: Teubner, 1883.
BERSTEIN S. Sur Une Classe d'Equations Fonctionnelles Aux Derives Partielles [J]. Izvestiya Rossiiskoi Akademii Nauk-Seriya Matematicheskaya, 1940, 4(1): 17-26.
LIONS J. Quelques Methods de Resolution Des Problems Aux Limites Non-linéaires [M]. Paris: Dunod, 1969.
STRAUSS W A. Nonlinear Wave Equations [M]. Providence RI: American Mathematical Society, 1989.
CHOI J Y, HONG K S, HUH C D. Vibration Control of an Axially Moving Strip by a Non-Linear Boundary Control [J]. IFAC Proceedings Volumes, 2002, 35(1): 1-6.
王跃, 梁金平, 索洪敏. 一类非局部近共振问题多重解的存在性[J]. 西南大学学报(自然科学版), 2018, 40(4): 53-58.
王跃, 索洪敏, 韦维. 无边界约束的一类新Kirchhoff型问题的古典解[J]. 数学物理学报, 2020, 40(4): 857-868. doi: 10.3969/j.issn.1003-3998.2020.04.004
王跃, 叶红艳, 雷俊, 等. 带线性项Kirchhoff型问题的无穷多古典解[J]. 广西师范大学学报(自然科学版), 2020, 38(6): 65-73.
WANG Y, SUO H M, LEI C Y. Multiple Positive Solutions for a Nonlocal Problems Involving Critical Exponent [J]. Electronic Journal of Differential Equations, 2017, 2017(275): 1-11.
LEI C Y, LIAO J F, SUO H M. Multiple Positive Solutions for a Nonlocal Problems Involving a Sign-Changing Potential [J]. Electronic Journal of Differential Equations, 2017, 2017(9): 1-8.
LEI C Y, CHU C M, SUO H M. Positive Solutions for a Nonlocal Problem with Singularity [J]. Electronic Journal of Differential Equations, 2017, 2017(85): 1-9.
王跃. 负模量基尔霍夫型问题进展[J]. 应用泛函分析学报, 2020, 22(4): 230-258.
王跃, 叶红艳, 索洪敏. 一类带Hardy-Sobolev临界指数的非局部问题正解的存在性[J]. 应用数学, 2019, 32(2): 452-456.
WANG Y, YANG X. Infinitely Many Solutions for a New Kirchhoff Type Equation with Subcritical Exponent [J]. Applicable Analysis, 2020, 2020: 1-14.
DUAN Y, SUN X, LI H Y. Existence and Multiplicity of Positive Solutions For a Nonlocal Problem [J]. The Journal of Nonlinear Sciences and Applications, 2017, 10(11): 6056-6061. doi: 10.22436/jnsa.010.11.40
王跃, 索洪敏, 熊宗洪, 等. 椭圆型广义Kirchhoff问题的多重解[J]. 扬州大学学报(自然科学版), 2020, 23(5): 19-22.
贾秀玲, 段誉. 一类带线性项非局部问题解的存在性与非存在性[J]. 西南师范大学学报(自然科学版), 2018, 43(10): 22-25.
李红英. 一类非局部问题的多解性[J]. 西南师范大学学报(自然科学版), 2017, 42(6): 24-27.
唐之韵, 欧增奇. 一类非局部问题解的存在性与多重性[J]. 西南大学学报(自然科学版), 2018, 40(10): 48-52.
PERERA K, ZHANG Z T. Nontrivial Solutions of Kirchhoff-Type Problems Via the Yang Index [J]. Journal of Differential Equations, 2006, 221(1): 246-255.
MOTE-JR C D. A Study of Band Saw Vibration [J]. Journal of the Frankin Institute, 1965, 279(6): 430-444.
EKELAND I. On the Variational Principle [J]. Journal of Mathematical Analysis and Applications, 1974, 47(2): 324-353.
PUCCI P, SERRIN J. A Mountain Pass Theorem [J]. Journal of Differential Equations, 1985, 60(1): 142-149.