CAJ | 학술논문

利用锥拉伸和锥压缩型的Krasnosel′skii不动点定理,证明了当λ在某区间内时,含下有界非线性项的一类三阶三点特征值问题至少有一个正解存在;且λ=1时,在适当条件下,建立了这类边值问题多解存在的充分条件,并获得一些新的存在性与多解性的结论.
이용추랍신화추압축형적Krasnosel′skii불동점정리,증명료당λ재모구간내시,함하유계비선성항적일류삼계삼점특정치문제지소유일개정해존재;차λ=1시,재괄당조건하,건립료저류변치문제다해존재적충분조건,병획득일사신적존재성여다해성적결론.
By using the Krasnosel′skii fixed point theorem of cone expansion-compression type,it is shown that a class of three-order three-point eigenvalue problem with bounded-below nonlinearly has at least one positive solution for λ in a compatible interval.When λ=1,under suitable conditions,the sufficient conditions of existence of multiple solutions for this class boundary value problem are established.Some new existence and multiplicity conclusions of solutions are obtained.