Ground state sign-changing solutions for elliptic equations with logarithmic nonlinearity

We study elliptic equations with logarithmic nonlinearity. With the help of the constraint variational method, quantitative deformation lemma and some new energy inequalities, we establish the existence of ground state solutions and ground state sign-changing solutions with precisely two nodal domains. Our result complements the existing ones on Schrodinger problems since the logarithmic nonlinearity is sign-changing, and satisfies neither the monotonicity condition nor Ambrosetti-Rabinowitz condition.