Multiple Positive Solutions for a Class of Integral Boundary Value Problem

Abstract

In this paper, the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem

with two parameters are established by using the Guo-Krasnoselskii's fixed-point theorem, where $f∈C$([0,1]×[0,+∞)×(−∞,0], [0,+∞)), $q(t)∈L$¹[0,1] is nonnegative, $α, β ∈ R$ and satisfy $β<2π$², $α$>0, $α/π$⁴+$β/π$²<1, $λ$_1,2=(−$β$∓$\sqrt{β^2+4α}$)/2. The corresponding examples are raised to demonstrate the results we obtained.