Symmetric positive solutions for nonlinear singular fourth-order eigenvalue problems with nonlocal boundary condition
By using a fixed point theorem in cones, the authors prove the existence of symmetric positive solutions of the fourth-order nonlocal boundary value problem \[ \begin{cases} u^{(4)}(t)-\lambda h(t)f(t,u,u'')=0,\,\,\,0<t<1,\\ u(0)=u(1)=\displaystyle\int_0^1a(s)u(s)\,ds,\\ u''(0)=u''(1)=\displaystyle\int_0^1b(s)u''(s)\,ds,\end{cases} \] where \(a,\,b\in L^1[0,1]\), \(\lambda>0\), \(h\) may be singular at \(t=0\) and/or \(t=1\) and \(f(t,x,y)\) may also have singularities at \(x=0\) and/or \(y=0\).
scientific article; zbMATH DE number 5701479