This paper is concerned with the following fourth-order three-point boundary value problem BVP \[ u^{\left(4\right)}\left(t\right)=f\left(t,u\left(t\right)\right),\quad t\in\left[0,1\right], \] \[ u'\left(0\right)=u''\left(0\right)=u\left(1\right)=0,\;u'''\left(\eta\right)+\alpha u\left(0\right)=0, \] where $f\in C\left(\left[0,1\right]\times\left[0,+\infty\right),\left[0,+\infty\right)\right)$ , $\alpha\in\left[0,6\right)$ and $\eta\in\left[\frac{2}{3},1\right)$. Although corresponding Green\textquoteright s function is sign-changing, we still obtain the existence of monotone positive solution under some suitable conditions on $f$ by applying iterative method. An example is also given to illustrate the main results.
Boundary value problem Green’s function Positive solution Iterative method Sign-changing
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 25 Aralık 2018 |
Gönderilme Tarihi | 27 Nisan 2018 |
Kabul Tarihi | 17 Aralık 2018 |
Yayımlandığı Sayı | Yıl 2018 Cilt: 1 Sayı: 2 |