Single-peak solutions for a subcritical Schrodinger equation with non-power nonlinearity

This paper deals with the following slightly subcritical Schrodinger equation: -Delta u +v (x)u =f(epsilon) (u),u > 0 in R-N, where v (x) is a nonnegative smooth function,f(epsilon) (u) =u(p/) [ln(e+u)](epsilon), p =N+2/N -2,epsilon > 0,N >= 7. Most of the previous works for the Schrodinger equations were mainly investigated for power-type nonlinearity. In this paper, we will study the case when the nonlinearity f(epsilon) (u) is a non-power nonlinearity. We show that, for.. small enough, there exists a family of single-peak solutions concentrating at the positive stable critical point of the potential v (x).