On an eigenvalue problem with variable exponents and sign-changing potential

摘要

In this paper we study a non-homogeneous eigenvalue problem involving variable growth conditions and a sign-changing potential. We prove that any $lambda>0$ sufficiently small is an eigenvalue of the nonhomogeneous eigenvalue problem egin{equation*} egin{cases} -{m div}(a(|abla u|) abla u)=lambda V(x)|u|^{q(x)-2}u, Omega, u=0, partialOmega. end{cases} end{equation*} The proofs of the main results are based on Ekeland's variational principle.