Another understanding of fourth-order four-point boundary-value problems

Electronic Journal of Differential Equations

关键词: Multipoint boundary value problem;    positive solution;    vector field;    third order differential equation;    Green function;    Krasnoselskii's fixed point theorem;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this article we investigate the existence of positive and/or negativesolutions of a classes of four-point boundary-value problems forfourth-order ordinary differential equations. The assumptions in thisarticle are more relaxed than the known assumptions. Our technique relies onthe continuum property (connectedness and compactness) of the solutionsfunnel (Knesser's Theorem), combined with the corresponding vector field'sones. This approach permits the extension of results (getting positivesolutions) to nonlinear boundary conditions, whenever the correspondingGreen's kernel is not of definite sign or there does not exist (see the lastCorollary).

【 授权许可】

Unknown