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arXiv · 2512.05426

Two abstract methods of lower and upper solutions with applications

Andrei Stan
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Abstract

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.

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Andrei Stan. 2025-12-05. Two abstract methods of lower and upper solutions with applications. https://arxiv.org/abs/2512.05426

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