Multiple solutions for a class of perturbed damped vibration problems
-
2911
Downloads
-
4993
Views
Authors
Mohamad Reza Heidari Tavani
- Department of Mathematics, Science and Research branch, Islamic Azad University, Tehran, Iran.
Ghasem A. Afrouzi
- Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran.
Shapour Heidarkhani
- Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran.
Abstract
The existence of three distinct weak solutions for a class of perturbed damped vibration problems
with nonlinear terms depending on two real parameters is investigated. Our approach is based on
variational methods.
Share and Cite
ISRP Style
Mohamad Reza Heidari Tavani, Ghasem A. Afrouzi, Shapour Heidarkhani, Multiple solutions for a class of perturbed damped vibration problems, Journal of Mathematics and Computer Science, 16 (2016), no. 3, 351-363
AMA Style
Tavani Mohamad Reza Heidari, Afrouzi Ghasem A., Heidarkhani Shapour, Multiple solutions for a class of perturbed damped vibration problems. J Math Comput SCI-JM. (2016); 16(3):351-363
Chicago/Turabian Style
Tavani, Mohamad Reza Heidari, Afrouzi, Ghasem A., Heidarkhani, Shapour. "Multiple solutions for a class of perturbed damped vibration problems." Journal of Mathematics and Computer Science, 16, no. 3 (2016): 351-363
Keywords
- Multiple solutions
- perturbed damped vibration problem
- critical point theory
- variational methods.
MSC
References
-
[1]
G. A. Afrouzi, S. Heidarkhani, S. Moradi , Perturbed elastic beam problems with nonlinear boundary conditions , Annal. Al. I. Cuza Univ. Math., (to appear),
-
[2]
F. Antonacci, P. Magrone, Second order nonautonomous systems with symmetric potential changing sign, Rend. Mat. Appl., 18 (1998), 367-379.
-
[3]
G. Bonanno, P. Candito , Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differential Equations, 244 (2008), 3031-3059.
-
[4]
G. Bonanno, G. DAgui, Multiplicity results for a perturbed elliptic Neumann problem , Abstr. Appl. Anal., 2010 (2010 ), 10 pages.
-
[5]
G. Bonanno, R. Livrea, Periodic solutions for a class of second-order Hamiltonian systems, Electron. J. Differential Equations, 2005 (2005), 13 pages.
-
[6]
G. Bonanno, R. Livrea, Multiple periodic solutions for Hamiltonian systems with not coercive potential , J. Math. Anal. Appl., 363 (2010), 627-638.
-
[7]
G. Bonanno, R. Livrea , Existence and multiplicity of periodic solutions for second order Hamiltonian systems depending on a parameter , J. Convex Anal., 20 (2013), 1075-1094.
-
[8]
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.
-
[9]
G. Chen, Nonperiodic damped vibration systems with asymptotically quadratic terms at infinity: infinitely many homoclinic orbits , Abstr. Appl. Anal., 2013 (2013 ), 7 pages.
-
[10]
G. Chen, Non-periodic damped vibration systems with sublinear terms at infinity: infinitely many homoclinic orbits , Nonlinear Anal., 92 (2013), 168-176.
-
[11]
H. Chen, Z. He , New results for perturbed Hamiltonian systems with impulses , Appl. Math. Comput., 218 (2012), 9489-9497.
-
[12]
G.-W. Chen, J. Wang, Ground state homoclinic orbits of damped vibration problems, Bound. Value Probl., 2014 (2014 ), 15 pages.
-
[13]
G. Cordaro , Three periodic solutions to an eigenvalue problem for a class of second order Hamiltonian systems , Abstr. Appl. Anal., 18 (2003), 1037-1045.
-
[14]
G. Cordaro, G. Rao, Three periodic solutions for perturbed second order Hamiltonian systems , J. Math. Anal. Appl., 359 (2009), 780-785.
-
[15]
G. DAgui, S. Heidarkhani, G. Molica Bisci, Multiple solutions for a perturbed mixed boundary value problem involving the one-dimensional p-Laplacian , Electron. J. Qual. Theory Diff. Eqns., 2013 (2013 ), 14 pages.
-
[16]
F. Faraci, Multiple periodic solutions for second order systems with changing sign potential, J. Math. Anal. Appl., 319 (2006), 567-578.
-
[17]
F. Faraci, R. Livrea, Infinitely many periodic solutions for a second-order nonautonomous system , Nonlinear Anal., 54 (2003), 417-429.
-
[18]
J. R. Graef, S. Heidarkhani, L. Kong, Infinitely many solutions for a class of perturbed second-order impulsive Hamiltonian systems, Acta Appl. Math., 139 (2015), 81-94.
-
[19]
J. R. Graef, S. Heidarkhani, L. Kong , Nontrivial periodic solutions to second-order impulsive Hamiltonian systems, Electron. J. Differential Equations, 2015 (2015), 17 pages.
-
[20]
S. Heidarkhani, G. A. Afrouzi, M. Ferrara, G. Caristi, S. Moradi, Existence results for impulsive damped vibration systems , Bull. Malays. Math. Sci. Soc., 2016 (2016 ), 20 pages.
-
[21]
J. Mawhin, M. Willem, Critical Point Theory and Hamiltonian Systems, Springer-Verlag, New York (1989)
-
[22]
P. H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems , Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38.
-
[23]
P. H. Rabinowitz, Variational methods for Hamiltonian systems, Handbook of Dynamical Systems vol. 1, Part A, 2002 (2002), 1091-1127.
-
[24]
J. Sun, H. Chen, J. J. Nieto, M. Otero-Novoa, The multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects , Nonlinear Anal., 72 (2010), 4575-4586.
-
[25]
C.-L. Tang, Periodic solutions of non-autonomous second order systems with \(\gamma\)-quasisubadditive potential, J. Math. Anal. Appl., 189 (1995), 671-675.
-
[26]
C.-L. Tang, Periodic solutions for nonautonomous second order systems with sublinear nonlinearity , Proc. Amer. Math. Soc., 126 (1998), 3263-3270.
-
[27]
C.-L. Tang, X.-P. Wu, Periodic solutions for a class of nonautonomous subquadratic second order Hamiltonian systems, J. Math. Anal. Appl., 275 (2002), 870-882.
-
[28]
X. Wu, J. Chen, Existence theorems of periodic solutions for a class of damped vibration problems, Appl. Math. Comput., 207 (2009), 230-235.
-
[29]
X. Wu, S. Chen, K. Teng, On variational methods for a class of damped vibration problems , Nonlinear Anal., 68 (2008), 1432-1441.
-
[30]
X. Wu, W. Zhang, Existence and multiplicity of homoclinic solutions for a class of damped vibration problems, Nonlinear Anal., 74 (2011), 4392-4398.
-
[31]
J. Xiao, J. J. Nieto, Variational approach to some damped Dirichlet nonlinear impulsive differential equations, J. Franklin Inst., 348 (2011), 369-377.
-
[32]
E. Zeidler, Nonlinear functional analysis and its applications, Vol. II: Linear monotone operators, Springer-Verlag, New York (1985)
-
[33]
W. Zou , Variant fountain theorems and their applications, Manuscripta Math., 104 (2001), 343-358.