Positive solutions of a nonlinear fourth order boundary value problem. (English) Zbl 1136.34024
The authors study the existence and nonexistence of positive solutions of the nonlinear fourth order boundary value problem
\[ y''''(t)=g(t)f(y(t)),\quad 0<t<1, \]
\[ u(0)=u''(0)=u'(1)=u''(1)=0, \]
where \(f:[0,\infty)\rightarrow [0,\infty)\) is continuous, \(g:[0,1]\rightarrow [0,\infty)\) is continuous such that \(\int^1_0 g(t)dt>0\). The main tool they used is the Guo-Krasnoselskii fixed point theorem on cones.
\[ y''''(t)=g(t)f(y(t)),\quad 0<t<1, \]
\[ u(0)=u''(0)=u'(1)=u''(1)=0, \]
where \(f:[0,\infty)\rightarrow [0,\infty)\) is continuous, \(g:[0,1]\rightarrow [0,\infty)\) is continuous such that \(\int^1_0 g(t)dt>0\). The main tool they used is the Guo-Krasnoselskii fixed point theorem on cones.
Reviewer: Ruyun Ma (Lanzhou)
MSC:
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
