Bernstein approximations of nonlinear Sturm-Liouville problems
This is an interesting article that deals with the Sturm-Liouville boundary value problem \[ u''(t)+\phi(t,u(t),u'(t),\lambda)=0,\quad t\in(0,1) \] with boundary conditions \(L(u)=0\). This may include nonlinear boundary value problems for some classes of ordinary differential equations. The main idea is to approximate these differential equations by finite dimensional Bernstein approximations given explicitely in the paper. The author uses a global bifurcation theorem to obtain existence results for nonlinear Sturm-Liouville problems. The paper, overall, interesting and useful, however, it is more suitable for specialists.
scientific article; zbMATH DE number 5669288