three-point third-order problems with a sign-changing nonlinear term
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ID: 252045
2014
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Abstract
In this article we study a well-known boundary value problem
$$\displaylines{
u'''(t) = f(t, u(t)), \quad 0 < t < 1, \cr
u(0) = u'(1/2) = u''(1)=0.
}$$
With $u'(\eta)=0$ in place of $u'(1/2)=0$, many authors studied the existence
of positive solutions of both the positone problems with $\eta \geq 1/2$ and
the semi-positone problems for $\eta > 1/2$. It is well-known that the standard
method successfully applied to the semi-positone problem with $\eta > 1/2$
does not work for $\eta =1/2$ in the same setting. We treat the latter as a
problem with a sign-changing term rather than a semi-positone problem.
We apply Krasnosel'skii's fixed point theorem [4] to obtain positive solutions.
| Reference Key |
henderson2014electronicthree-point
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|---|---|
| Authors | ;Johnny Henderson;Nickolai Kosmatov |
| Journal | icsoft 2006 - 1st international conference on software and data technologies, proceedings |
| Year | 2014 |
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