manuscripta mathematica

, Volume 21, Issue 1, pp 81–100

Eine Existenzaussage für asymptotisch lineare Störungen eines Fredholmoperators mit Index O


  • G. Hetzer
    • Lehrstuhl C für MathematikRWTH Aachen
  • V. Stallbohm
    • Lehrstuhl C für MathematikRWTH Aachen

DOI: 10.1007/BF01176903

Cite this article as:
Hetzer, G. & Stallbohm, V. Manuscripta Math (1977) 21: 81. doi:10.1007/BF01176903


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.

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© Springer-Verlag 1977