Positive solutions of a fourth-order differential equation with multipoint boundary conditions (Q2354633)

The author studies the fourth-order multipoint boundary value problem \[ x^{(4)}(t) = \lambda f (t, x(t), x'(t ), x''(t)), \quad 0 < t < 1, \] \[ x^{(2k+1)}(0) = 0, \;\;\;x^{(2k)}(1) = \sum\limits_{i=1}^{m-2}\alpha_{ki}x^{(2k)}(\eta_{ki} ), \quad k = 0, 1. \] Sufficient conditions for the existence of positive solutions are obtained by using fixed point theorems in cones.