Abstract
Let be a given domain and . We show that the validity of Poincaré inequality implies the solvability of degenerate elliptic eigenvalue problems , for sufficiently small . Our method exploits Ekeland’s Variational Principle and Palais–Smale sequences which are adapted to our quite general settings. We are assuming that the involved weights belong to the so-called -class, introduced by Kufner and Opic in 1984. Nonexistence of positive solutions of (S) for some choice of weights is also discussed.
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