On the application of measure of noncompactness to existence theorems
For the integral equation (1) below we prove the existence on an interval of a solution with values in a Banach space , belonging to the class , . Further, the set of solutions is shown to be a compact one in the sense of Aronszajn.
For the integral equation (1) below we prove the existence on an interval of a solution with values in a Banach space , belonging to the class , . Further, the set of solutions is shown to be a compact one in the sense of Aronszajn.
We give sufficient conditions for the existence of at least one integrable solution of equation . Our assumptions and proofs are expressed in terms of measures of noncompactness.
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