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<p>In this paper, we present two abstract methods for constructing a lower and an upper solution for a fixed point equation. The first method applies when the nonlinear operator is a composition of a linear and a nonlinear mapping, while the second method applies when the nonlinear operator satisfies an inequality of Harnack type. An application is provided for each method.</p>

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Two Abstract Methods of Lower and Upper Solutions with Applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月17日

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  • Andrei Stan

摘要

In this paper, we present two abstract methods for constructing a lower and an upper solution for a fixed point equation. The first method applies when the nonlinear operator is a composition of a linear and a nonlinear mapping, while the second method applies when the nonlinear operator satisfies an inequality of Harnack type. An application is provided for each method.