, Volume 21, Issue 1, pp 81-100

Eine Existenzaussage für asymptotisch lineare Störungen eines Fredholmoperators mit Index O

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Abstract

Let X, Y be Banach spaces, L: X ⊃ Dom(L)→Y a linear Fredholm operator with Fredholm index zero, and T a asymptotic linear k-set contraction with k∈[0, 1(L)), where 1(L) denotes the lower bound of L with respect to the set-measure of noncampactness. Using coincidence degree we deduce a Fredholm alternative for the equation Lx=Tx+y (y∈Y), which involves the results of [11] and [17] in the case X=Y and L=Id. Applications are given for a functional differential equation of neutral type and for a boundary value problem of a second order differential equation.