Download PDF - Existence of three anti-periodic solutions for second-order impulsive differential inclusions with two parametersAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Existence of three anti-periodic solutions for second-order impulsive differential inclusions with two parameters

Authors 1, 2, 3, 3

Affiliations

  1. Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran
  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran
  3. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Abstract

Applying two three critical points theorems, we prove the existence of at least three anti-periodic solutions for a second-order impulsive differential inclusion with a perturbed nonlinearity and two parameters.

Keywords

ENG
differential inclusion, impulsive, anti-periodic solution, non-smooth critical point theory

Bibliography

  1. G. Bonanno and P. Candito, Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Diff. Equ. 244 (2008), 3031-3059. doi: 10.1016/j.jde.2008.02.025
  2. G. Bonanno and 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. doi: 10.1080/00036810903397438
  3. H.L. Chen, Antiperiodic wavelets, J. Comput. Math. 14 (1996), 32-39.
  4. F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983.
  5. F.J. Delvos and L. Knoche, Lacunary interpolation by antiperiodic trigonometric polynomials, BIT, 39 (1999), 439-450. doi: 10.1023/A:1022314518264
  6. P. Djakov and B. Mityagin, Simple and double eigenvalues of the Hill operator with a two-term potential, J. Approx. Theory, 135 (2005), 70-104. doi: 10.1016/j.jat.2005.03.004
  7. L.H. Erbe and W. Krawcewicz, Existence of solutions to boundary value problems for impulsive second order differential inclusions, Rocky Mountain J. Math. 22 (1992), 519-539. doi: 10.1216/rmjm/1181072746
  8. M. Frigon and D. O'Regan, First order impulsive initial and periodic problems with variable moments, J. Math. Anal. Appl. 233 (1999), 730-739. doi: 10.1006/jmaa.1999.6336
  9. A. Iannizzotto, Three critical points for perturbed nonsmooth functionals and applications, Nonlinear Anal. 72 (2010), 1319-1338. doi: 10.1016/j.na.2009.08.001
  10. A. Iannizzotto, Three periodic solutions for an ordinary differential inclusion with two parameters, Ann. Polon. Math. 103 (2012), 89-100. doi: 10.4064/ap103-1-7
  11. A. Kristály, Infinitely many solutions for a differential inclusion problem in ℝN, J. Diff. Equ. 220 (2006), 511-530. doi: 10.1016/j.jde.2005.02.007
  12. A. Kristály, W. Marzantowicz and C. Varga, A non-smooth three critical points theorem with applications in differential inclusions, J. Glob. Optim. 46 (2010), 49-62. doi: 10.1007/s10898-009-9408-0
  13. S.A. Marano and D. Motreanu, Infinitely many critical points of non-differentiable functions and applications to a Neumann-type problem involving the p-Laplacian, J. Diff. Equ. 182 (2002), 108-120. doi: 10.1006/jdeq.2001.4092
  14. D. Motreanu and P.D. Panagiotopoulos, Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities, Kluwer Academic Publishers, Dordrecht, 1999.
  15. B. Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math. 113 (2000), 401-410. doi: 10.1016/S0377-0427(99)00269-1
  16. Y. Tian and J. Henderson, Three anti-periodic solutions for second-order impulsive differential inclusions via nonsmooth critical point theory, Nonlinear Anal. 75 (2012), 6496-6505. doi: 10.1016/j.na.2012.07.025
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
2013/33/2
Export to PBN, Opens in new tab
Pages:
115-133
Main language of publication
English
Received
2013-02-19
Published
2013

DOI: 10.7151/dmdico1150

Exact and natural sciences