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PDF(423 KB)
具非自治微小扰动的脉冲方程三个古典解的存在性
The Existence of Triple Classical Solutions to Impulsive Problems with Small Non-autonomous Perturbations
在半直线无穷区间上，我们研究具有微小非自治扰动项的脉冲方程边值问题的古典解，应用变分方法和相应的临界点理论得到了三个古典解的存在性.
We study the existence of solutions to nonlinear impulsive boundary value problems with small non-autonomous perturbations on the half-line. We show the existence of at least three distinct classical solutions by using variational methods and a three critical points theorem.
半直线 / 非自治扰动 / 三解 {{custom_keyword}} /
half-line / non-autonomous perturbation / triple solutions {{custom_keyword}} /
[1] Chen H., Sun J., An application of variational method to second-order impulsive differential equation on the half-line, Appl. Math. Comput., 2010, 217:1863-1869.
[2] Bonanno G., Marano S. A., On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal., 2010, 89:1-10.
[3] Bonanno G., Riccobono G., Multiplicity results for Sturm-Liouville boundary value problems, Appl. Math. Comput., 2009, 210:294-297.
[4] Bonanno G., Chinn? A., Existence of three solutions for a perturbed two-point boundary value problem, Appl. Math. Lett., 2010, 23:807-811.
[5] Liu J., Zhao Z., Variational approach to existence of weak solutions to second-order singular impulsive problems, Acta Math. Sci. Ser. A, 2016, 36(3):521-530.
[6] Liu J., Zhao Z., Variational approach to second-order damped Hamiltonian systems with impulsive effects, J. Nonlinear Sci. Appl., 2016, 9:3459-3472.
[7] Liu J., Zhao Z., Existence of positive solutions to a singular boundary-value problem using variational methods, Electro. J. Differ. Equ., 2014, 135:1-9.
[8] Liu J., Zhao Z., An application of variational methods to second order impulsive differential equation with derivative dependence, Electro. J. Differ. Equ., 2014, 62:1-13.
[9] Liu J., Zhao Z., Existence of classical solutions to impulsive problems under Cerami condition, Acta Math. Sinica, Chin. Ser., 2016, 59(5):609-622.
[10] Nieto J., O'Regan D., Variational approach to impulsive differential equations, Nonlinear Anal., 2009, 10:680-690.
[11] Nieto J., Variational formulation of a damped Dirichlet impulsive problem, Appl. Math. Lett., 2010, 23:940-942.
[12] Sun J., Chen H., Variational method to the impulsive equation with Neumann boundary conditions, Bound.Value Probl., 2009, 2009, Article ID 316812, 17 pages.
[13] Tian Y., Ge W., Variational methods to Sturm-Liouville boundary value problem for impulsive differential equations, Nonlinear Anal., 2010, 72:277-287.
[14] Tian Y., Ge W., Applications of variational methods to boundary value problem for impulsive differential equations, Proc. Edinburgh Math. Soc., 2008, 51:509-527.
国家自然科学基金（11571197，11301303，11601269）；教育部人文社会科学研究项目（16YJC630070）；山东省自然科学基金（ZR2017MA048，ZR2018MG002）；泰山学者工程专项经费项目（tsqn20161041）；山东省高等学校科技计划项目（J16LI11）；山东省高等学校优势学科人才团队培育计划（1716009）和山东财经大学青年优秀人才支持计划
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