Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 1, Pages 83-91

On nonlinear boundary value problems with deviating arguments and discontinuous right hand side

B. C. Dhage1 and S. Heikkilä2

1Mahatma Gandhi Mahavidyalaya, Department of Mathematics, Ahmedpur, 413515, India
2University of Oulu, Department of Mathematics, Oulu 57 SF-90570, Finland

Received 1 December 1992; Revised 1 March 1993

Copyright © 1993 B. C. Dhage and S. Heikkilä. 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.


In this paper we shall study the existence of the extremal solutions of a nonlinear boundary value problem of a second order differential equation with general Dirichlet/Neumann form boundary conditions. The right hand side of the differential equation is assumed to contain a deviating argument, and it is allowed to possess discontinuities in all the variables. The proof is based on a generalized iteration method.