Positive solutions for a fourth-order boundary value problem (Q355681)

Summary: This paper deals with the existence and multiplicity of positive solutions for the fourth-order boundary value problem \[ \begin{aligned} u^{(4)}& = f(t, u, u', -u'', u'''),\\ u(0)& = u'(1) = u'''(0) = u''(1) = 0.\end{aligned} \] Here, \(f \in C([0, 1] \times \mathbb R^4_+, \mathbb R_+)\) \((\mathbb R_+ := [0, +\infty))\). We use the fixed point index theory to establish our main results based on a priori estimates achieved by using some integral identities and integral inequalities.