Linear and Nonlinear Nonlocal Boundary Value Problems for Differential-operator Equations

This study focuses on nonlocal boundary value problems (BVP) for linear and nonlinear elliptic differential-operator equations (DOE) that are defined in Banachvalued function spaces. The considered domain is a region with varying bound and depends on a certain parameter. Some conditions that guarantee the maximal Lpregularity and Fredholmness of linear BVP, uniformly with respect to this parameter, are presented. This fact implies that the appropriate differential operator is a generator of an analytic semigroup. Then, by using these results, the existence, uniqueness, and maximal smoothness of solutions of nonlocal BVP for nonlinear DOE are shown. These results are applied to nonlocal boundary value problems for regular elliptic partial differential equations, finite and infinite systems of differential equations on cylindrical domains, in order to obtain the algebraic conditions that guarantee the same properties.