Cone-Constrained Linear Equations in Banach Spaces

This paper presents necessary and sufficient conditions for the existence of solutions to cone-constrained linear equations in some function spaces. These conditions yield, in particular, the classical Fredholm alternative for compact operators. We use a formulation that under some conditions permits to apply the Generalized Farkas Theorem of Craven and Koliha. The Poissson Equation for stochastic (Markov) kernels, the Volterra and Fredholm equations for non-compact operators in Lₚ spaces, are among the particular cases of potential application.