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PDF(414 KB)
PDF(414 KB)
四阶脉冲弹性梁方程非平凡弱解的存在数量
The Numbers of Nontrivial Weak Solutions to Fourth-order Impulsive Elastic Beam Equations
本文研究了一类具有脉冲项的四阶弹性梁微分方程边值问题，在非线性项不连续的情况下利用变分方法结合相应的临界点定理得到了非平凡弱解的存在数量，最后给出具体的例子，结合牛顿迭代法来验证所得到的结论.
In this paper, the numbers of nontrivial solutions to superlinear fourthorder impulsive elastic beam equations are obtained. We get two theorems via variational methods and corresponding two-critical-points theorems. Combining with the Newton-iterative method, two examples are presented to illustrate the value of the obtained theorems.
弹性梁方程 / 脉冲 / 变分方法 {{custom_keyword}} /
elastic beam equations / impulsive effects / variational methods {{custom_keyword}} /
[1] Bonanno G., Relations between the mountain pass theorem and local minima, Adv. Nonlinear Anal., 2012, 1:205-220.
[2] Bonanno R., Candito P., Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differ. Equations, 2008, 12:3031-3059.
[3] Bonanno G., D'Aguì G., Two Non-Zero Solutions for Elliptic Dirichlet Problems, Anal. Anwend., 2016, 35:449-464.
[4] Bonanno G., Di Bella B., A boundary value problem for fourth-order elastic beam equations, J. Math. Anal. Appl., 2008, 343:1166-1176.
[5] Bonanno G., Iannizzotto A., Marras M., Two positive solutions for superlinear Neumann problems with a complete Sturm-Liouville operator, J. Convex. Anal., 2018, 25:421-34.
[6] Bonanno G., Livrea R., Multiple periodic solutions for Hamiltonian systems with not coercive potential, J. Math. Anal. Appl., 2010, 363:627-638.
[7] D'Aguì G., Sciammetta A., Tornatore E., Two non-zero solutions for Sturm-Liouville equations with mixed boundary conditions, Nonlinear Anal. Real World Appl., 2019, 47:324-331.
[8] Liu J., Yu W., Two solutions to superlinear Hamiltonian systems with impulsive effects, Appl. Math. Lett., 2020, 102:106162.
[9] Liu J., Zhao Z., An application of variational methods to second-order impulsive differential equation with derivative dependence, Electron. J. Differ. Eq., 2014, 2014:1-13.
[10] Liu J., Zhao Z., Existence of classical solutions to impulsive boundary value problems under Cerami condition, Acta Math. Sin., Chin. Ser., 2016, 59:609-622.
[11] Liu J., Zhao Z., Multiple solutions for impulsive problems with non-autonomous perturbations, Appl. Math. Lett., 2017, 64:143-149.
[12] Liu J., Zhao Z., Variational approach to second-order damped Hamiltonian systems with impulsive effects, J. Nonlinear Sci. Appl., 2016, 9:3459-3472.
[13] Liu J., Zhao Z., Yu W., The existence of triple classical solutions to impulsive problems with small nonautonomous perturbations, Acta Math. Sin., Chin. Ser., 2019, 62:441-448.
[14] Liu J., Zhao Z., Zhang T., Multiple solutions to damped Hamiltonian systems with impulsive effects, Appl. Math. Lett., 2019, 91:173-180.
[15] Nieto J., Variational formulation of a damped Dirichlet impulsive problem, Appl. Math. Lett., 2010, 23:940-942.
[16] Nieto J., O'Regan D., Variational approach to impulsive differential equations, Nonlinear Anal., 2009, 10:680-690.
[17] Sun J., Chen H., Nieto J., et al., Multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects, Nonlinear Anal. Real World Appl., 2010, 72:4575-4586.
[18] Sun J., Chen H., Yang L., Variational methods to fourth-order impulsive differential equations, J. Appl. Math. Comput., 2011, 35:323-340.
[19] Xie J., Luo Z., Solutions to a boundary value problem of a fourth-order impulsive differential equation, Bound. Value Probl., 2013, 154:1-18.
国家自然科学基金（11571197，11601269）；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）；山东财经大学青年优秀人才支持计划；山东省高等学校优势学科人才团队培育计划（1716009）；泰山学者工程专项经费（tsqn20161041）
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