科研之友
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摘要
We study the logarithmic Schrodinger equation with the sign-changing potential function. It is known that the corresponding functional is not well defined in H-1(R-N), but by imposing some condition on V(x), we can show that the functional is well defined in a subspace of H-1(R-N). Then, the existence and multiplicity of solutions is obtained by using variational methods. We remark that the existence of solutions is deeply influenced by the sign of Q(x). Published under license by AIP Publishing.
