Abstract
A linear, completely nonhomogeneous, generally nonlocal, multipoint problem is investigated for a second-order ordinary integro-differential equation with generally nonsmooth coefficients, satisfying some general conditions like p-integrability and boundedness. A system of three integro-algebraic equations named the adjoint system is introduced for the solution. The solvability conditions are found by the solutions of the homogeneous adjoint system in an “alternative theorem”. A version of a Green’s functional is introduced as a special solution of the adjoint system. For the problem with a nontrivial kernel also a notion of a generalized Green’s functional is introduced by a projection operator defined on the space of solutions. It is also shown that the classical Green and Cauchy type functions are special forms of the Green’s functional.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.