Oscillating solutions of a nonlinear fourth order ordinary differential equation (Q853990)

The authors consider the boundary value problem \[ \begin{gathered} u^{(4)}+ au''+ g(t, u', u'', u''')= p(t),\quad 0< t< T,\\ u^{(j)}(0)= u^{(j)}(T)\quad\text{for }j= 0,\dots, 3,\end{gathered}\tag{\(*\)} \] where \(g\) is continuous and \(p\in L^2(0,T)\). Applying coincidence degree theory and the method of lower and upper solutions, the authors prove the existence of at least one solution to \((*)\) under suitable conditions.