(L-lambda N) is A-proper for (lambdain[0,1]).
If (L_{1}^{-1}) is compact, then (L-lambda N) is A-proper for each (lambdain[0,1]).
Theorem 2.1 If L : dom L → Y is Fredholm of index zero, let L − λ N be A-proper for λ ∈ [ 0, 1 ].
Proof It is again easy to show that L − λ N is A-proper for λ ∈ [ 0, 1 ] by [[20], Lemma 2(a)].
Proof First, we note that L, as defined, is Fredholm of index zero, L 1 − 1 is compact by the Arzela-Ascoli theorem and thus L − λ N is A-proper for λ ∈ [ 0, 1 ] by [[20], Lemma 2(a)].
(liminf_{xrightarrow+infty}min_{tin [0,1]} frac{f t,x)}{x}>4), (limsup_{xrightarrow0^max_{tin [0,1]} frac{f t,x)}{x}<0), First, we note that L, as defined, is Fredholm of index zero, (L_{1}^{-1}) is compact by Arzela-Ascoli theorem and thus (L-lambda N) is A-proper for (lambdain[0,1]) by Lemma 2.1.
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