Existence of positive solutions for a nonlinear fourth order boundary value problem

Volume 81 / 2003

Ruyun Ma Annales Polonici Mathematici 81 (2003), 79-84 MSC: Primary 34B18. DOI: 10.4064/ap81-1-7


We study the existence of positive solutions of the nonlinear fourth order problem $$ \eqalign{ &u^{(4)}(x)=\lambda a(x)f(u(x)),\cr &u(0)=u'(0)=u' '(1)=u' ' '(1)=0,\cr}$$ 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.


  • Ruyun MaDepartment of Mathematics
    Northwest Normal University
    Lanzhou 730070, Gansu, P. R. China

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