On boundary value problem for fractional differential equations

Document Type : Research Paper

Authors

1 Department of Mathematics‎, ‎Faculty of Sciences‎, ‎Razi University‎, ‎67149 Kermanshah‎, ‎Iran.

2 Department of Mathematics‎, ‎Faculty of Sciences‎, ‎Razi‎ University,‎ ‎67149 Kermanshah‎, ‎Iran.

Abstract

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.

Keywords

Main Subjects

References

T. Bartsch, In_nitely many solutions of a symmetric Dirichlet problem, Nonlinear Anal. 20 (1993), no. 10, 1205--1216.
T. Bartsch and S.J. Li, Critical point theory for asymptotically quadratic functional and applications to problems with resonance, Nonlinear Anal. 28 (1997), no. 3, 419--441.
G. Bonanno, R. Rodriguez-Lopez and S. Tersian, Existence of solutions to boundary value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal. 17 (2014), no. 3, 717--744.
A.M.A. El-Sayed, Nonlinear functional differential equations of arbitrary orders, Non-linear Anal. 33 (1998), no. 2, 181--186.
F. Jiao and Y. Zhou, Existence of solutions for a class of fractional boundary value problems via critical point theory, Comput. Math. Appl. 62 (2011), no. 3, 1181--1199.
F. Jiao and Y. Zhou, Existence results for fractional boundary value problem via critical point theory, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 22 (2012), no. 4, 1--17.
A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies 204, Elsevier Science, Amsterdam, 2006.
A.A. Kilbas and J.J. Trujillo, Differential equations of fractional order: methods, results and problems I, Appl. Anal. 78 (2001), no. 1-2, 153--192.
A.A. Kilbas and J.J. Trujillo, Differential equations of fractional order: methods, results and problems II, Appl. Anal. 81 (2002), no. 2, 435--493.
Y.N. Li, H.R. Sun and Q.G. Zhang, Existence of solutions to fractional boundary-value problems with a parameter, Electron. J. Differential Equations 2013 (2013), no. 141, 12 pages.
J. Nieto and D. O'Regan, Variational approach to impulsive differential equations, Non-linear Anal. Real World Appl. 10 (2009), no. 2, 680--690.
I. Podlubny, Fractional Differential Equations, Academic Press, NewYork, 1999.
R. Rodriguez- Lopez and S. Tersian, Multiple solutions to boundary value problem for impulsive fractional differential equations, Fract. Calc. Appl. Anal. 17 (2014), no. 4, 1016--1038.
C. Torres, Existence of solutions for fractional Hamiltonian systems, Electron. J. Differential Equations 2013 (2013), no 259, 12 pages.
M. Willem, Minimax Theorems, Birkhäuser, Boston, 1996.
Z.Q. Wang, On a superlinear elliptic equation, Ann. Inst. H. Poincare Anal. Non Lineaire 8 (1991), no. 1, 43--57.
Bulletin of the Iranian Mathematical Society
Volume 43, Issue 3
June 2017
Pages 789-805

Files

History

  • Receive Date: 13 August 2015
  • Revise Date: 19 February 2016
  • Accept Date: 19 February 2016

Share

How to cite

Statistics