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Applications of Schauder's fixed point theorem to singular differential equations
Bulletin of the London Mathematical Society, 2007In this paper, we study the existence of positive periodic solutions to second-order singular differential equations. The proof relies on Schauder’s fixed point theorem. Our results show that in some situations weak singularities can help create periodic solutions, as pointed out by Torres [J. Differential Equations 232 (2007) 277–284].
Jifeng Chu, Pedro J. Torres
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The Schauder-Tychonoff Fixed Point Theorem
2019In order to prove the main result of this chapter, the Schauder-Tychonoff fixed point theorem, we first need a definition and a lemma.
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Schauder's fixed point theorem and Pontryagin maximum principle
Izvestiya: MathematicsWe prove the Pontryagin maximum principle for a general optimal control problem. The main ingredient of the proof is the abstract lemma on an inverse function, which is proved via the Schauder fixed-point theorem. Under this approach, the proof of the Pontryagin maximum principle is quite short and transparent.
Avakov, Evgeny R. +1 more
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A generalization of the Schauder fixed point theorem via multivalued contractions.
2001Summary: We establish a fixed point theorem for a continuous function \(f:X\to E\), where \(E\) is a Banach space and \(X\subseteq E\). Our result, which involves multivalued contractions, contains the classical Schauder fixed point theorem as a special case. An application is presented.
CUBIOTTI, Paolo, DI BELLA, Beatrice
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Solutions of Fredholm type integral equations via the classical Schauder fixed point theorem
Journal of Integral Equations and Applications, 2021Merve TEMİZER Ersoy
exaly