Geodesic
Existence of positive solutions for a nonlinear fourth order boundary value problem
Ruyun Ma1
1 Department of Mathematics Northwest Normal University Lanzhou 730070, Gansu, P. R. China
Annales Polonici Mathematici, Tome 81 (2003) no. 1, pp. 79-84.

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

We study the existence of positive solutions of the nonlinear fourth order problem $$ \eqalign{ ^{(4)}(x)=\lambda a(x)f(u(x)),\cr (0)=u'(0)=u' '(1)=u' ' '(1)=0,\cr}$$ where $a: [0,1]\rightarrow \mathbb R$ may change sign, $f(0)>0$, and $\lambda>0$ is sufficiently small. Our approach is based on the Leray–Schauder fixed point theorem.
DOI : 10.4064/ap81-1-7
Keywords: study existence positive solutions nonlinear fourth order problem eqalign lambda u where rightarrow mathbb may change sign lambda sufficiently small approach based leray schauder fixed point theorem

Ruyun Ma 1

1 Department of Mathematics Northwest Normal University Lanzhou 730070, Gansu, P. R. China 
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Ruyun Ma. Existence of positive solutions for a nonlinear fourth order
 boundary value problem. Annales Polonici Mathematici, Tome 81 (2003) no. 1, pp. 79-84. doi : 10.4064/ap81-1-7. http://geodesic.mathdoc.fr/articles/10.4064/ap81-1-7/

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