A nonlocal boundary value problem for a class of nonlinear equations of mixed type

Abstract

Nonlocal boundary-value problems for second order linear and nonlinear differential equations of mixed type in a bounded multidimensional cylindrical domain are considered. Uniqueness and existence of a weak solution in the linear case are established. Applying these results and Schauder's fixed point theorem existence of a weak solution in the nonlinear case is proved. A uniqueness result is also established.