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MR1646309 (99h:34028) 34B15 (34C10 34L30 35J65 47H15)
Drábek, Pavel; Takáč, Peter A counterexample to the Fredholm alternative for the $p$-Laplacian. Proc. Amer. Math. Soc. 127 (1999), no. 4, 1079–1087.
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