Positive solutions to fourth-order singular boundary value problems with integral boundary conditions in abstract spaces

Abstract

Under various weaker conditions, we establish various results on the existence of positive solutions to fourth-order singular boundary value problems with integral boundary conditions in abstract spaces. The arguments are based upon a specially constructed cone and the fixed point theory in cone for a strict set contraction operator. Our results improve and extend that obtained in [X. Zhang, M. Feng, W. Ge, Existence results for nonlinear boundary value problems with integral boundary conditions in Banach spaces, Nonlinear Anal. 69 (2008) 3310–3321; Y. Liu, Multiple positive solutions to fourth-order singular boundary value problems in abstract spaces, Electron. J. Diff. Eqns. 120 (2004) 1–13], even in the scalar spaces.