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Here the Leray–Schauder degree theory is used to solve some BVPs for ODEs. More precisely: §9.1.1 is devoted to the existence of periodic solutions to ODEs as well as to delay equations considered as perturbations of ODEs; §9.1.2 outlines Krasnoselski’s theory about guiding functions; §9.2 studies conjugate multipoint BVPs by appealing to the sign property of the associated Green functions. An interesting peculiarity: some results point out the possibility that the linear differential operators and/or the boundary conditions may differ from equation to equation in the same system.

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Applications to ODEs (Using Operators in Function Space)

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  • 发表日期：

    2026年

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  • Giovanni Vidossich

摘要

Here the Leray–Schauder degree theory is used to solve some BVPs for ODEs. More precisely: §9.1.1 is devoted to the existence of periodic solutions to ODEs as well as to delay equations considered as perturbations of ODEs; §9.1.2 outlines Krasnoselski’s theory about guiding functions; §9.2 studies conjugate multipoint BVPs by appealing to the sign property of the associated Green functions. An interesting peculiarity: some results point out the possibility that the linear differential operators and/or the boundary conditions may differ from equation to equation in the same system.