The Method of Lower and Upper Solutions for Second, Third, Fourth, and Higher Order Boundary Value Problems
The Method of Lower and Upper Solutions for Second, Third, Fourth, and Higher Order Boundary Value Problems
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DOI：
10.1006/jmaa.1994.1250
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发表时间：
1994-07
影响因子：
1.3
通讯作者：
A. Cabada
中科院分区：
文献类型：
--
作者：
A. Cabada
本文研究了问题u（n）（t）= n（t，u（t））;u（i）（a）-u（i）（B）=λ i ∈ R ; i=0，. n−1。其中，k是Caratheodory函数。本文给出了当n=2（若α≥β），n=3（若α≤β或α≥β）和n=4（若α≤β）时，在下解α和上解β之间存在解的充要条件.进一步，当α≤β时，我们得到了n=2k≥6的充分条件.
Abstract In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u (n) (t)=ƒ(t, u(t));u (i) (a)−u (i) (b)=λ i ∈ R ; i=0, ..., n−1. Where ƒ is a Caratheodory function. We obtain necessary and sufficient conditions in ƒ to guarantee the existence of solutions between a lower solution α and an upper solution β for n=2 (if α≥β), n=3 (either α≤β or α≥β) and n=4 (if α≤β). Furthermore, we obtain sufficient conditions in ƒ for n=2k≥6 when α≤β.