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2013 | 33 | 2 | 115-133
Tytuł artykułu

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

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Języki publikacji
EN
Abstrakty
EN
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.
Twórcy
  • Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran
  • School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran
autor
  • Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
autor
  • Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
Bibliografia
  • [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 $ℝ^N$, 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
Typ dokumentu
Bibliografia
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