Resumen de Normalized Solutions of Schrödinger Equations with Combined Nonlinearities

Ting-ting Dai, Zeng-Qi Ou, Ying Lv

• In this paper, we study the nonlinear Schrödinger equation with L2-norm constraint −u = λu + |u|p−2u + h(x)|u| q−2u in RN , RN u2dx = c2, where c > 0, N ≥ 3, 1 ≤ q < 2 < p < 2 + 4 N , h ∈ L 2 2−q (RN ) and λ ∈ R is Lagrange multiplier, which appears due to the mass constraint |u|2 = c. We use barycentric functions and minimax method to prove that for any c > 0, there exists a positive solution u ∈ H1(RN ) for some λ < 0.