Positive Solutions of a Fourth-Order Differential Equation with Multipoint Boundary Conditions

Abstract

This paper is devoted to the study of the following fourth-order multipoint boundary value problem: $$\left\{\begin{array}{ll} x^{(4)}(t) = \lambda f(t,x(t),x^{\prime }(t) ,x^{\prime \prime}(t)),\quad 0 < t < 1,& \\ x^{(2k+1)}(0)=0,x^{(2k)}(1)=\sum_{i=1}^{m-2}\alpha_{ki}x^{(2k)}(\eta_{ki}),&(k = 0, 1). \end{array}\right. $$ We obtain some sufficient conditions for the existence of at least one or triple positive solutions by using the fixed point theory in cone.