Geodesic
Existence of solutions for a fourth-order boundary-value problem
Electronic journal of differential equations, Tome 2008 (2008)
Zbl   EuDML
In this paper, we use the lower and upper solution method to obtain an existence theorem for the fourth-order boundary-value problem

$\displaylines{ u^{(4)}(t)=f(t,u(t),u'(t),u''(t),u'''(t)),\quad 01,\cr u(0)=u'(1)=u''(0)=0,\quad u'''(1)=g\big(\int^1_0u''(t)d\theta(t)\big), }$

where $f : [0,1]\times \mathbb{R}^4 \to \mathbb{R}, g : \mathbb{R}\to \mathbb{R}$ are continuous and may be nonlinear, and $\int^1_0u''(t)d\theta(t)$ denotes the Riemann-Stieltjes integral.
Classification : 34B15
Keywords: fourth-order boundary-value problem, upper and lower solution, Riemann-stieltjies integral, Nagumo-type condition 
Liu,  Yang. Existence of solutions for a fourth-order boundary-value problem. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a69/
@article{EJDE_2008__2008__a69,
     author = {Liu,  Yang},
     title = {Existence of solutions for a fourth-order boundary-value problem},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1172.34305},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a69/}
}
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