<it>A priori</it> estimates for the existence of a solution for a multi-point boundary value problem

Abstract

Let , , , , with be given. Let be such that , be given. This paper is concerned with the problem of obtaining Poincaré type a priori estimates of the form . The study of such estimates is motivated by the problem of existence of a solution for the Caratheodory equation , , satisfying boundary conditions . This problem was studied earlier by Gupta et al. (Jour. Math. Anal. Appl. 189 (1995), 575–584) when the 's, all had the same sign.

Keywords

• <it>A priori</it> estimates
• Multi-point boundary value problem
• Leray&#8211;Schauder continuation theorem
• Caratheodory's conditions