Title: Existence of Solutions for a Certain Boundary Value Problem Associated to a Fourth Order Differential Inclusion
Author(s): Aurelian Cernea
Pages: 27-33
Cite as:
Aurelian Cernea, Existence of Solutions for a Certain Boundary Value Problem Associated to a Fourth Order Differential Inclusion, Int. J. Anal. Appl., 14 (1) (2017), 27-33.


Existence of solutions for a fourth order differential inclusion with cantilever boundary conditions is investigated. New results are obtained when the right hand side has convex or non convex values.

Full Text: PDF



  1. J.P. Aubin and H. Frankowska, Set-valued Analysis, Birkhäuser, Basel, 1990.

  2. A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86.

  3. A. Cabada, R. Precup, L. Saavedra and S.A. Tersian, Multiple positive solutions to a fourth-order boundary value problem, Electronic J. Differ. Equ. 2016 (2016), Art. 254.

  4. J.A. Cid, D. Franco and F. Minhos, Positive fixed points and fourth-order equations, Bull. Lond. Math. Soc. 41 (2009), 72-78.

  5. R. Enguica and L. Sanchez, Existence and localization of solutions for fourth-order boundary value problems, Electron. J. Differ. Equ. 2007 (2007), Art. 127.

  6. A.F. Filippov, Classical solutions of differential equations with multivalued right hand side, SIAM J. Control 5 (1967), 609-621.

  7. M. Frignon and A. Granas, Theoremes dexistence pour les inclusions differentielles sans convexite, C. R. Acad. Sci. Paris, Ser. I 310 (1990), 819-822.

  8. J.R. Graef, L. Kong, Q. Kong and B. Yang, Positive solutions to a fourth order boundary value problem, Results Math. 59 (2011), 141-155.

  9. A. Lasota and Z. Opial, An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Math., Astronom. Physiques 13 (1965), 781-786.

  10. F. Li, Q. Zhang and Z. Liang, Existence and multiplicity of solutions of a kind of fourth-order boundary value problem, Nonlinear Anal. 62 (2005), 803-816.

  11. D. O’ Regan, Fixed point theory for closed multifunctions, Arch. Math. (Brno) 34 (1998), 191-197.

  12. L. Yang, H. Chen and X. Yang, The multiplicity of solutions for fourth-order equations generated from a boundary condition, Appl. Math. Lett. 24 (2011), 1599-1603.