Three anti-periodic solutions for second-order impulsive differential inclusions via nonsmooth critical point theory

Nonlinear Analysis, Theory, Methods and Applications

Volumn 75, Issue 18, 2012, Pages 6496-6505

  Tian, Yu ^a,b   Henderson, Johnny ^b  

^a BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

^b BAYLOR UNIVERSITY   (United States)

Author keywords

Anti periodic solution; Differential inclusions; Impulsive; Nonsmooth critical point theory

Indexed keywords

ANTI-PERIODIC SOLUTIONS; CRITICAL POINTS; DIFFERENTIAL INCLUSIONS; IMPULSIVE; NON-LINEARITY; NON-SMOOTH; NONSMOOTH CRITICAL POINT THEORY; SECOND ORDERS; TWO PARAMETER;

MATHEMATICAL TECHNIQUES; NONLINEAR ANALYSIS;

DIFFERENTIAL EQUATIONS;

EID: 84865688489     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2012.07.025     Document Type: Article

References (23)

1. B. Ricceri A three critical points theorem revisited Nonlinear Anal. 70 2009 3084 3089
2. D.D. Bainov, and P.S. Simeonov Systems with Impulsive Effect Ellis Horwood Series: Mathematics and its Applications 1989 Ellis Horwood Chichester
3. M. Benchohra, J. Henderson, and S.K. Ntouyas Impulsive Differential Equations and Inclusions vol. 2 2006 Hindawi Publishing Corporation New York
4. V. Lakshmikantham, D.D. Bainov, and P.S. Simeonov Theory of Impulsive Differential Equations 1989 World Scientific Singapore
5. A.M. Samoilenko, and N.A. Perestyuk Impulsive Differential Equations World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises vol. 14 1995 World Scientific New Jersey
6. J.P. Aubin, and A. Cellina Differential Inclusions 1984 Springer, Birkhäuser New York, Basal
7. V.I. Blagodatskikh, A.F. Filippov, Differential inclusions and optimal control, in: Topology, Differential Equations, Dynamical Systems (Tr. Mat. Inst. Steklova, 169 (1985), Nauka, Moscow, pp. 194-252) (in Russian).
8. A.I. Bulgakov Integral inclusions with nonconvex images and their applications to boundary value problems for differential inclusions Mat. Sb. 183 10 1992 63 86
9. A.I. Bulgakov, and L.I. Tkach Perturbation of a convex-valued operator by a Hammerstein-type multivalued mapping with nonconvex images, and boundary value problems for functional differential inclusions Mat. Sb. 189 6 1998 3 32
10. D.A. Carlson Carathéodory's method for a class of dynamic games J. Math. Anal. Appl. 276 2 2002 561 588
11. A. Iannizzotto Three critical points for perturbed nonsmooth functionals and applications Nonlinear Anal. 72 2010 1319 1338
12. A. Iannizzotto Three periodic solutions for an ordinary differential inclusion with two parameters Ann. Polon. Math. 103 1 2011 89 100
13. N.N. Krasovskii, and A.I. Subbotin Game - Theoretical Control Problems Springer Series in Soviet Mathematics 1988 Springer New York
14. M.D.P. Monteiro Marques Differential Inclusions in Nonsmooth Mechanical Problems Progress in Nonlinear Differential Equations and their Applications 1993 Birkhäuser Basel
15. G.V. Smirnov Introduction to the Theory of Differential Inclusions Graduate Studies in Mathematics vol. 41 2002 American Mathematical Society Rhode Island
16. F.J. Delvos, and L. Knoche Lacunary interpolation by antiperiodic trigonometric polynomials BIT 39 1999 439 450
17. H.L. Chen Antiperiodic wavelets J. Comput. Math. 14 1996 32 39
18. 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
19. L.H. Erbe, and W. Krawcewicz Existence of solutions to boundary value problems for impulsive second order differential inclusions Rocky Mountain J. Math. 22 2 1992 519 539
20. M. Frigon, and D. O'Regan First order impulsive initial and periodic problems with variable moments J. Math. Anal. Appl. 233 2 1999 730 739
21. F.H. Clarke Optimization and Nonsmooth Analysis 1983 Wiley New York
22. D. Motreanu, and P.D. Panagiotopoulos Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities 1999 Kluwer Academic Publishers Dordrecht
23. B. Ricceri Existence of three solutions for a class of elliptic eigenvalue problems Math. Comput. Modelling 32 2000 1485 1494