Method of upper and lower solutions for nonlinear lntegrodifferential equations of mixed type in banach spaces

Abstract

In this paper, the authors use upper and lower solutions to investigate the extremal solutions of two-point boundary value problems for second order nonlinear integrodifferential equations of mixed type in Banach spaces. One main existence theorem is obtained and an example in a certain infinite dimensional space is given.

Keywords:

• Integrodifferential equations
• upper and lower solutions
• measure of noncompactness, strict set contraction, fixed points