Infinitely Many Solutions to a Fourth-Order Impulsive Differential Equation with Two Control Parameters

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DOI: 10.46793/KgJMat2205.789H


In this article, we give some new criteria to guarantee the infinitely many solutions for a fourth-order impulsive boundary value problem. Our main tool to ensure the existence of infinitely many solutions is the classical Ricceri’s Variational Principle.


Infinitely many solutions, impulsive differential equations, critical points, variational methods.


[1]   G. A. Afrouzi, A. Hadjian and V. Radulescu, Variational approach to fourth-order impulsive differential equations with two control parameters, Results Math. 65 (2014), 371–384.

[2]   G. A. Afrouzi, A. Hadjian and V. Radulescu, Variational analysis for Dirichlet impulsive differential equations with oscillatory nonlinearity, Port. Math. 70(3) (2013), 225–242.

[3]   S. Heidarkhani, G. A. Afrouzi, M. Ferrara and S. Moradi, Variational approaches to impulsive elastic beam equations of Kirchhoff type, Complex Variables and Elliptic Equations 61(7) (2016), 931–968.

[4]   S. Heidarkhani, M. Ferrara, A. Salari and M. Azimbagirad, A variational approach to perturbed elastic beam problems with nonlinear boundary conditions, Math. Reports 18(68) (2016), 573–589.

[5]   B. Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math. 113 (2000), 401–410.

[6]   J. Sun, H. Chen and L. Yang, Variational methods to fourth-order impulsive differential equations, J. Appl. Math. Comput. 35 (2011), 323–340.

[7]   Y. Tian and W. Ge, Applications of variational methods to boundary value problem for impulsive differential equations, Proc. Edinburgh Math. Soc. 51 (2008), 509–527.

[8]   J. Xie and Z. Luo, Solutions to a boundary value problem of a fourth-order impulsive differential equation, Bound. Value Probl. 2013 (2013), 1–14.