科研之友
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摘要
We find a Green's function for the singular third-order three-point BVP
u'''(t) = -a(t)f(t, u(t)), u(0) = u'(1) = u ''(eta) = 0
where 0 <= eta < 1/2. Then we apply the classical Krasnosel'skii's fixed point theorem for finding solutions in a cone. Although this problem Green's function is not positive, the obtained solution is still positive and increasing. Our techniques rely on a combination of a fixed point theorem and the properties of the corresponding vector field.
- 出版日期2007
