Normalized solutions for logarithmic Schrodinger equation with a perturbation of power law nonlinearity

We study the existence of normalized solutions to the following logarithmic Schrodinger equation -Delta u+lambda u=alpha ulogu(2)+mu|u|(p-2)u, x is an element of R-N, under the mass constraint integral(RN)u(2)dx=c(2), where alpha,mu is an element of R, N >= 2, p>2, c>0 is a constant, and lambda is an element of R appears as Lagrange multiplier. Under different assumptions on alpha, mu, p and c, we prove the existence of ground state solutions and excited state solutions. The asymptotic behavior of the ground state solution as mu -> 0 is also investigated. Our results include the case alpha<0 or mu<0, which is less studied in the literature.