Positive Solutions for a Fourth-Order Boundary Value Problem

Abstract EN

This paper deals with the existence and multiplicity of positive solutions for the fourth-order boundary value problem u(4)=f(t,u,u′,−u′′, u′′′),u(0)=u′(1)=u′′′(0)=u′′(1)=0.

Here f∈C([0,1]×ℝ+4,ℝ+)(ℝ+:=[0,+∞)).

We use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing some integral identities and integral inequalities.