Green and Generalized Green¿s Functionals of Linear Local and Nonlocal Problems for Ordinary Integro-differential Equations

• Autores: Seyidali S. Akhiev
• Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 95, Nº. 2, 2007, págs. 73-93
• Idioma: inglés
• DOI: 10.1007/s10440-006-9056-z
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• Resumen

  • 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.