Local existence of multiple positive solutions to a singular cantilever beam equation
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.
scientific article; zbMATH DE number 5644912
scientific article