Infinitely many solutions for Schrödinger equations with Hardy potential and Berestycki-Lions conditions

Abstract

In this article, we investigate the following Schrödinger equation: −Δu−μ∣x∣2u=g(u)inRN,-\Delta u-\frac{\mu }{{| x| }^{2}}u=g\left(u)\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{N}, where N≥3N\ge 3, μ∣x∣2\frac{\mu }{{| x| }^{2}} is called the Hardy potential and gg satisfies Berestycki-Lions conditions. If 0<μ<(N−2)240\lt \mu \lt \frac{{\left(N-2)}^{2}}{4}, we will take symmetric mountain pass approaches to prove the existence of infinitely many solutions of this problem.

Keywords

• berestycki-lions conditions
• hardy potential
• infinitely many solutions
• variation method
• symmetric mountain pass
• 35jxx
• 46txx
• 49j35
• 49j40