237 research outputs found
On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent
We consider the nonlinear eigenvalue problem in , on
, where is a bounded open set in \RR^N with smooth
boundary and , are continuous functions on such that
, , and
for all . The main result of this paper
establishes that any sufficiently small is an eigenvalue of the
above nonhomogeneous quasilinear problem. The proof relies on simple
variational arguments based on Ekeland's variational principle
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