Existence of Multiple Solutions for Elliptic Equations with Indefinite Potential

• Lifeng Yin ^[1] ; Shuai Jiang ^[1]
  1. [1] Xiamen University
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
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• Resumen

  • In this paper, the following modified fourth-order Schrödinger equation α2u − u + V(x)u − u(u2) = g(u), in RN , and quasilinear Schrödinger equation with α = 0 are discussed. The nonlinearity is subquadratic, i.e., lim |t|→∞ g(t) t2 = 0, 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.