English

Two abstract methods of lower and upper solutions with applications

Functional Analysis 2025-12-08 v1

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.

Keywords

Cite

@article{arxiv.2512.05426,
  title  = {Two abstract methods of lower and upper solutions with applications},
  author = {Andrei Stan},
  journal= {arXiv preprint arXiv:2512.05426},
  year   = {2025}
}
R2 v1 2026-07-01T08:10:43.885Z