Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

THREE SOLUTIONS FOR A SECOND-ORDER STURM-LIOUVILLE EQUATION WITH IMPULSIVE EFFECTS

  • HAGHSHENAS, HADI (Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran) ;
  • AFROUZI, GHASEM A. (Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran)
  • Received : 2019.08.06
  • Accepted : 2020.04.06
  • Published : 2020.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this article, a second-order Sturm-Liouville problem with impulsive effects and involving the one-dimensional p-Laplacian is considered. The existence of at least three weak solutions via variational methods and critical point theory is obtained.

Keywords

References

  1. G.A. Afrouzi, A. Hadjian and S. Heidarkhani, Infinitely Many Solutions for a Mixed Doubly Eigenvalue Boundary Value Problem, Mediterr. J. Math. 10 (2013), 1317-1331. https://doi.org/10.1007/s00009-013-0243-7
  2. G.A. Afrouzi, A. Hadjian and V. Radulescu, A variational approach of Sturm-Liouville problems with the nonlinearity depending on the derivative, Bound. Value Probl. (2015), 1-17.
  3. D. Averna, R. Salvati, Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian, J. Math. Anal. Appl. 298 (2004), 245-260. https://doi.org/10.1016/j.jmaa.2004.05.012
  4. L. Bai, B. Dai, Three solutions for a p-Laplacian boundary value problem with impulsive effects, Appl. Math. Comput. 217 (2011), 9895-9904. https://doi.org/10.1016/j.amc.2011.03.097
  5. G. Bonanno, A. Chinni, Existence of three solutions for a perturbed two-points boundary value problem, Appl. Math. Lett. 23 (2010), 807-811. https://doi.org/10.1016/j.aml.2010.03.015
  6. G. Bonanno, G. Riccobono, Multiplicity results for Sturm-Liouville boundary value problems, Appl. Math. comput. 210 (2009), 294-297. https://doi.org/10.1016/j.amc.2008.12.081
  7. G. Bonanno, S.A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal. 89 (2010), 1-10. https://doi.org/10.1080/00036810903397438
  8. H. Chen, J. Sun, An application of variational method to second-order impulsive differential equation on the half-line, Appl. Math. Comput. 217 (2010), 1863-1869. https://doi.org/10.1016/j.amc.2010.06.040
  9. G. D;Agui, Existence results for a mixed boundary value problem with Sturm-Liouville equation, Adv. Pure Appl. Math. 2 (2011), 237-248. https://doi.org/10.1515/APAM.2010.043
  10. V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of Impulsive Differential Equations, Series Modern Appl. Math., Vol. 6, World Scientific, Teaneck, NJ, 1989.
  11. B. Ricceri, On a three critical points theorem, Arch. Math. (Basel) 75 (2000), 220-226. https://doi.org/10.1007/s000130050496
  12. Y. Tian, W. Ge, Second-order Sturm-Liouville boundary value problem involving the one-dimensional p-Laplacian, Rocky Mountain J. Math. 38 (2008), 309-327. https://doi.org/10.1216/RMJ-2008-38-1-309
  13. Y. Tian, W. Ge, Applications of variational methods to boundary value problem for impulsive differential equations, Proc. Edinburgh Math. Soc. 51 (2008), 509-527. https://doi.org/10.1017/S0013091506001532
  14. J. Xie, Z. Lou, Multiple solutions for a second-order impulsive Sturm-Liouville equation, Abstr. Appl. Anal. (2013), 1-6.
  15. E. Zeidler, Nonlinear Functional Analysis and its Applications, Springer, Berlin, 1990.