The paper deals with the periodic boundary value problem (1) $L_4 x(t) + a(t)x(t) \in F(t,x(t))$, $t\in J= [a,b]$, (2) $L_i x(a)= L_i x(b)$, $i=0,1,2,3$, where $L_0x(t)= a_0x(t)$, $L_ix(t)=a_i(t)L_{i-1}x(t)$, $i=1,2,3,4$, $a_0(t)= a_4(t)=1$, $a_i(t)$, $i=1,2,3$ and $a(t)$ are continuous on $J$, $a(t)\geq 0$, $a_i(t)>0$, $i=1,2$, $a_1(t)= a_3(t)\cdot F(t,x): J \times R \to$\{nonempty convex compact subsets of $R$\}, $R= (-\infty , \infty )$. The existence of such periodic solution is proven via Ky Fan's fixed point theorem.
@article{107607,
author = {Marko \v Svec},
title = {Periodic boundary value problem of a fourth order differential inclusion},
journal = {Archivum Mathematicum},
volume = {033},
year = {1997},
pages = {167-171},
zbl = {0914.34015},
mrnumber = {1464311},
language = {en},
url = {http://dml.mathdoc.fr/item/107607}
}
Švec, Marko. Periodic boundary value problem of a fourth order differential inclusion. Archivum Mathematicum, Tome 033 (1997) pp. 167-171. http://gdmltest.u-ga.fr/item/107607/
On nonoscillatory solutions of functional differential equations with a general deviating argument, Hiroshima Math. J. 8 (1978), 49-62. (1978) | MR 0466865 | Zbl 0387.34048