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<p>The celebrated Amann three solutions theorem is extended to semilinear operator equations in ordered normed spaces. The main result is used to provide sufficient conditions for the existence of multiple solutions of boundary value problems for resonant first- and second-order differential equations and for a class of abstract equations involving linear CMO-maps.</p>

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Amann’s three solutions theorems for semilinear operator equation and applications

  • 期刊论文

  • 发表日期：

    2025年11月25日

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  • Feng Wang,
  • José Ángel Cid,
  • Mirosława Zima

摘要

The celebrated Amann three solutions theorem is extended to semilinear operator equations in ordered normed spaces. The main result is used to provide sufficient conditions for the existence of multiple solutions of boundary value problems for resonant first- and second-order differential equations and for a class of abstract equations involving linear CMO-maps.