International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 1, Pages 127-137
Solvability of a fourth-order boundary value problem with periodic boundary conditions II
Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439-4801, USA
Received 1 August 1989; Revised 17 December 1989
Copyright © 1991 Chaitan P. Gupta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a function satisfying Caratheodory's conditions and
. This paper is concerned with the solvability of the fourth-order fully quasilinear boundary
with . This problem was studied earlier by
the author in the special case when was of the form , i.e., independent of , , .
It turns out that the earlier methods do not apply in this general case. The conditions need to be related to
both of the linear eigenvalue problems
and with periodic boundary conditions.