Monotone iterative technique and symmetric positive solutions for a fourth-order boundary value problem

Authors:
Minghe Pei;Sung Kag Chang
Affiliations:
Department of Mathematics, Beihua University, JiLin City 132013, PR China;Department of Mathematics, Yeungnam University, Kyongsan, 712-749, Republic of Korea
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2010

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Abstract

The purpose of this paper is to investigate the existence of symmetric positive solutions for a class of fourth-order boundary value problem: {y^(^4^)(t)=f(t,y(t)),t@?[0,1],y(0)=y(1)=y^'(0)=y^'(1)=0. By using a monotone iterative technique, we proved that the above boundary value problem has symmetric positive solutions under certain conditions. In particular these solutions are obtained via the iteration procedures.