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<p>In this paper, we establish new Lyapunov-type inequalities for the radial Schrödinger equation, motivated by their relevance in stability analysis and quantum mechanical models. A Hartman-Wintner type inequality is derived, providing a sharper bound than the classical Bargmann inequality (1952). These results yield new disconjugacy criteria with direct implications for the qualitative behavior of solutions to Schrödinger-type equations. To demonstrate the effectiveness of the approach, we present applications to the identification of zero-free intervals of solutions, supported by numerical illustrations.</p>

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Lyapunov-type inequalities, disconjugacy, and zero-free intervals for the radial Schrödinger equation

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Mohamed Jleli,
  • Bessem Samet

摘要

In this paper, we establish new Lyapunov-type inequalities for the radial Schrödinger equation, motivated by their relevance in stability analysis and quantum mechanical models. A Hartman-Wintner type inequality is derived, providing a sharper bound than the classical Bargmann inequality (1952). These results yield new disconjugacy criteria with direct implications for the qualitative behavior of solutions to Schrödinger-type equations. To demonstrate the effectiveness of the approach, we present applications to the identification of zero-free intervals of solutions, supported by numerical illustrations.