Abstract. In this paper we investigate a general boundary value problem, which can be rewritten to the coincidence problem of the form $L(x)= F(x)$, where $L$ is a Fredholm operator of nonnegative index and $F$ is not necessarily compact map. We apply a homotopy invariant called a coincidence index.
AMSclassification. 34G20, 34B15, 47H09, 55M20
Keywords. Fredholm operator, boundary value problem in Banach space, fixed point index.