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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)),u(0)=u ' (0)=u '' (1)=u ''' (1)=0,

where q:(0,1)[0,) 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.

MSC:
34B16Singular nonlinear boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
74K10Rods (beams, columns, shafts, arches, rings, etc.) in solid mechanics
47N20Applications of operator theory to differential and integral equations
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