The existence of positive solutions of the nonlinear fourth order problemu (4)(x)=λa(x)f(u(x)), u(0)=u′(0)=u′(1)=u(1)=0is studied, where a:[0,1]→R may change sign, f(0)>0,λ>0 is sufficiently small. Our ...The existence of positive solutions of the nonlinear fourth order problemu (4)(x)=λa(x)f(u(x)), u(0)=u′(0)=u′(1)=u(1)=0is studied, where a:[0,1]→R may change sign, f(0)>0,λ>0 is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem.展开更多
In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It is proved that such a problem has at least two positive solutions u...In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The proof relies on a nonlinear alternative of Leray- Schauder type and Krasnoselskii fixed point theorem in cones.展开更多
文摘The existence of positive solutions of the nonlinear fourth order problemu (4)(x)=λa(x)f(u(x)), u(0)=u′(0)=u′(1)=u(1)=0is studied, where a:[0,1]→R may change sign, f(0)>0,λ>0 is sufficiently small. Our approach is based on the Leray-Schauder fixed point theorem.
基金The work was supported by science fundation for young teachers of Northeast Normal University (20060108).
文摘In this article, the author is devoted to establish the multiplicity of positive periodic solutions to second-order singular differential systems. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The proof relies on a nonlinear alternative of Leray- Schauder type and Krasnoselskii fixed point theorem in cones.
