Solutions of Sturm-Liouville boundary value problems for higher-order differential equations (Q2454978)

The article is concerned with a nonlinear boundary value problem of the form \[ x^{(n)}(t)= f(t, x(t),\dots, x^{(n-1)}(t))+ r(t), \] \[ x^{(i)}(0)= 0,\qquad i= 0,\dots, p-2, \] \[ x^{(j)}(1)= 0,\qquad j= p+1,\dots, n-1, \] \[ \alpha x^{(p-1)}(0)-\beta x^{(p)}(0)=\gamma x^{(p)}(1)=\delta x^{(p-1)}(1)= 0. \] The author gives sufficient conditions for the existence of at least one solution. Illustrative examples are given with a polynomial nonlinearity \(f\).