Geodesic
Existence Theorems for a Fourth Order Boundary Value Problem
A. El-Haffaf1
1 Département de Mathématiques Faculté des Sciences Université d'Oran B.P. 1524 Es-Senia, Oran, Algeria
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 2, pp. 135-148

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

This paper treats the question of the existence of solutions of a fourth order boundary value problem having the following form: $$\eqalign{ {x^{(4)}}(t) + f(t,x(t),x' '(t)) = 0,\ \quad 0 t 1,\cr (0) = x'(0) = 0,\ \quad {x' '(1) = 0},\ \quad {{x^{(3)}}(1) = 0}. }$$ 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.
DOI : 10.4064/ba57-2-7
Keywords: paper treats question existence solutions fourth order boundary value problem having following form eqalign t quad quad quad boundary value problems similar type considered assumed function space times mathbb mathbb main tool proof leray schauder nonlinear alternative

A. El-Haffaf 1

1 Département de Mathématiques Faculté des Sciences Université d'Oran B.P. 1524 Es-Senia, Oran, Algeria 
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A. El-Haffaf. Existence Theorems for a Fourth Order Boundary Value Problem. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 2, pp. 135-148. doi: 10.4064/ba57-2-7

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