Existence of three anti-periodic solutions for second-order impulsive differential inclusions with two parameters
S. Heidarkhani; G.A. Afrouzi; A. Hadjian
Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2013)
- Volume: 33, Issue: 2, page 115-133
- ISSN: 1509-9407
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topS. Heidarkhani, G.A. Afrouzi, and A. Hadjian. "Existence of three anti-periodic solutions for second-order impulsive differential inclusions with two parameters." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 33.2 (2013): 115-133. <http://eudml.org/doc/270208>.
@article{S2013,
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.},
author = {S. Heidarkhani, G.A. Afrouzi, A. Hadjian},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {differential inclusion; impulsive; anti-periodic solution; non-smooth critical point theory},
language = {eng},
number = {2},
pages = {115-133},
title = {Existence of three anti-periodic solutions for second-order impulsive differential inclusions with two parameters},
url = {http://eudml.org/doc/270208},
volume = {33},
year = {2013},
}
TY - JOUR
AU - S. Heidarkhani
AU - G.A. Afrouzi
AU - A. Hadjian
TI - Existence of three anti-periodic solutions for second-order impulsive differential inclusions with two parameters
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2013
VL - 33
IS - 2
SP - 115
EP - 133
AB - 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.
LA - eng
KW - differential inclusion; impulsive; anti-periodic solution; non-smooth critical point theory
UR - http://eudml.org/doc/270208
ER -
References
top- [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 Zbl1149.49007
- [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 Zbl1194.58008
- [3] H.L. Chen, Antiperiodic wavelets, J. Comput. Math. 14 (1996), 32-39. Zbl0839.42014
- [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 Zbl0931.42003
- [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 Zbl1080.34066
- [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 Zbl0784.34012
- [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 Zbl1186.35087
- [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 Zbl1248.34015
- [11] A. Kristály, Infinitely many solutions for a differential inclusion problem in , J. Diff. Equ. 220 (2006), 511-530. doi: 10.1016/j.jde.2005.02.007 Zbl1194.35523
- [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 Zbl1188.90252
- [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. Zbl1060.49500
- [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 Zbl0946.49001
- [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 Zbl1254.34026
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