On existence of multiple normalized solutions to a class of elliptic problems in whole RN

In this paper, we study the existence of multiple normalized solutions to the following class of elliptic problems - Δ u = λ u + h ( ϵ x ) f ( u ) , in R N , ∫ R N | u | 2 d x = a 2 , where a , ϵ > 0 , λ ∈ R is an unknown parameter that appears as a Lagrange multiplier, h : R N → [ 0 , ∞ ) is a continuous function, and f is continuous function with L 2 -subcritical growth. It is proved that the numbers of normalized solutions are at least the numbers of global maximum points of h when ϵ is small enough.