## Local existence of multiple positive solutions to a singular cantilever beam equation.(English)Zbl 1191.34031

The authors study existence and multiplicity of positive solutions to the fourth-order problem
$u^{(4)}=q(t)f(t, u(t), u'(t)),\quad u(0)=u'(0)=u''(1)=u'''(1)=0,$
where $$q:(0,1)\rightarrow [0, \infty)$$ is continuous with $$q(t)>0$$ in $$(0,1)$$, $$f$$ is allowed to be singular at $$t=0,~t=1$$,  $$u=0,~ v=0$$. The main tool is the Guo-Krasnoselskii fixed point theorem in cones.
Reviewer: Ruyun Ma (Lanzhou)

### MSC:

 34B16 Singular nonlinear boundary value problems for ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 47N20 Applications of operator theory to differential and integral equations
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### References:

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