Existence results for a model of nonlinear beam on elastic bearings

Applied Mathematics Letters

Volumn 13, Issue 5, 2000, Pages 11-15

  Ma, T F ^a  

^a STATE UNIVERSITY OF MARINGÁ   (Brazil)

Author keywords

Elastic beam; Fourth order ODE; Kirchhoff equation

Indexed keywords

EID: 0003151743     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(00)00026-4     Document Type: Article

References (11)

1. Kirchhoff G. Vorlessungen über Mathematiche Physik: Mechanik. 1876;Teubner, Leipzig.
2. Doppel K., Pflüger K., Herfort W. A nonlinear beam equation arising in the theory of bluff bodies. Z. Anal. Anwend. 16:1997;945-960.
3. Medeiros L.A. On a new class of nonlinear wave equations. J. Math. Anal. Appl. 69:1979;252-262.
4. Aftabizadeh A.R. Existence and uniqueness theorems for fourth order boundary value problems. J. Math. Anal. Appl. 116:1986;415-426.
5. Agarwal R.P. Boundary Value Problems for Higher Order Differential Equations. 1986;World Scientific, Singapore.
6. Gupta C.P. Existence and uniqueness theorems for a fourth order boundary value problem of Sturm-Liouville type. Diff. Int. Equations. 4:1991;397-410.
7. Sanchez L. Boundary value problems for some fourth order ordinary differential equations. Applicable Analysis. 38:1990;161-177.
8. Feireisl E. Nonzero time periodic solutions to an equation of Petrovsky type with nonlinear boundary conditions: Slow oscillations of beams on elastic bearings. Ann. Sc. Norm. Sup. Pisa. 20:1993;133-146.
9. Grossinho M.R., Ma T.F. Symmetric equilibria for a beam with a nonlinear elastic foundation. Portugaliae Mathematica. 51:1994;375-393.
10. Grossinho M.R., Ma T.F. Nontrivial solutions for a fourth order ODE with singular boundary conditions. Bainov D. Proceedings of the Seventh International Colloquium on Differential Equations. 1997;123-130 VSP, Netherlands.
11. Mawhin J. Critical point theory and nonlinear differential equations. Vosmansky J., Zlamal M. Differential Equations and Their Applications, Equadiff 6 Lect. Notes in Math. 1192. 1986;49-58 Springer-Verlag, New York.