Existence Theorems for a Fourth Order Boundary Value Problem

Volume 57 / 2009

A. El-Haffaf Bulletin Polish Acad. Sci. Math. 57 (2009), 135-148 MSC: 34B15, 34B14, 34B10. DOI: 10.4064/ba57-2-7


This paper treats the question of the existence of solutions of a fourth order boundary value problem having the following form: $$\eqalign{ &{x^{(4)}}(t) + f(t,x(t),x' '(t)) = 0,\ \quad 0 < t < 1,\cr &x(0) = x'(0) = 0,\ \quad {x' '(1) = 0},\ \quad {{x^{(3)}}(1) = 0}. }$$ Boundary value problems of very similar type are also considered. It is assumed that $f$ is a function from the space $C( {[ {0,1} ] \times \mathbb R^2,\mathbb R})$. The main tool used in the proof is the Leray–Schauder nonlinear alternative.


  • A. El-HaffafDépartement de Mathématiques
    Faculté des Sciences
    Université d'Oran
    B.P. 1524 Es-Senia, Oran, Algeria

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