Existence of Multiple Solutions for Elliptic Equations with Indefinite Potential.

In this paper, the following modified fourth-order Schrödinger equation α Δ 2 u - Δ u + V (x) u - u Δ (u 2) = g (u) , in R N , <graphic href="12346_2023_888_Article_Equ36.gif"></graphic> and quasilinear Schrödinger equation with α = 0 are discussed. The nonlinearity is subquadratic, i.e., lim | t | → ∞ g (t) t 2 = 0 , <graphic href="12346_2023_888_Article_Equ37.gif"></graphic> and the potential V is indefinite in sign. By variational methods, we will prove the existence of multiple solutions if α ≠ 0 and N ≤ 6 or α = 0 and N ≥ 3 . [ABSTRACT FROM AUTHOR]