The Unique Periodic Solution of Abel’s Differential Equation by Ni Hua

“…In this paper, the existence of a periodic solution for Abel’s differential equation is obtained first by using the fixed-point theorem. Then, by constructing the Lyapunov function, the uniqueness and stability of the periodic solution of the equation are obtained.…”
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Counting Periodic Points in Parallel Graph Dynamical Systems by Juan A. Aledo, Ali Barzanouni, Ghazaleh Malekbala, Leila Sharifan, Jose C. Valverde

“…Actually, periodic points of different periods cannot coexist, and a fixed point theorem is also known. In addition, an upper bound for the number of periodic points of F has been given. …”
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Approximate Controllability of Fractional Nonlinear Hybrid Differential Systems via Resolvent Operators by Mohammed M. Matar

“…The results are obtained by using resolvent and sectorial operators technique via Dhage fixed point theorem.…”
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Positive Periodic Solution of Second-Order Coupled Systems with Singularities by Tiantian Ma

“…Our approach is based on fixed point theorem in cones. Examples are given to illustrate the main result.…”
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Multiplicity of positive solutions for a third-order boundary value problem with nonlocal conditions of integral type by Sergey Smirnov

“…We prove the existence of multiple positive solutions for a nonlinear third-order nonlocal boundary value problem by applying Krasnosel’skii’s fixed point theorem. To illustrate the applicability of the obtained results, we consider an example.…”
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Convexity of Solutions for an Iterative Equation in Banach Spaces by Xiaobing Gong

“…By applying Schauder's fixed point theorem we investigate the existence of increasing (decreasing) solutions of the iterative equation and further give conditions under which those solutions are convex or concave. …”
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Fixed points and self-reference by Raymond M. Smullyan

“…It is shown how Gödel's famous diagonal argument and a generalization of the recursion theorem are derivable from a common construation. The abstract fixed point theorem of this article is independent of both metamathematics and recursion theory and is perfectly comprehensible to the non-specialist.…”
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Existence of C1-Positive Solutions for a Class of Second-Order Impulsive Differential Equations by Hong Li

“…In this study, under some inequality conditions, necessary and sufficient conditions, using fixed-point theorem in cones, are established for the existence of C1-positive solutions for a class of second-order impulsive differential equations. …”
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Results for Twin Singular Nonlinear Problems with Damping Term by Youwei Zhang

“…By using the functional type cone expansion and compression fixed-point theorem in cones, some new and general results on the existence of positive solution for twin singular boundary value problems with damping term are obtained. …”
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Exponential Dichotomy of the Two-Dimensional Linear Differential System by Ni Hua, Wang Jing, Bai Min

“…A sufficient condition for the exponential dichotomy of the linear system is given by the fixed point theorem and variable substitution, and some new results are obtained.…”
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A Bordism Viewpoint of Fiberwise Intersections by Gun Sunyeekhan

“…Moreover, we prove the converse of fiberwise Lefschetz fixed point theorem.…”
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Singular boundary value problem on infinite time scale

“…An existence theorem of positive solutions is established by using the Schauder fixed point theorem and perturbation and operator approximation method, which resolves the singularity successfully and differs from those of some papers. …”
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Existence of Weak Solutions for Fractional Integrodifferential Equations with Multipoint Boundary Conditions by Haide Gou, Baolin Li

“…By combining the techniques of fractional calculus with measure of weak noncompactness and fixed point theorem, we establish the existence of weak solutions of multipoint boundary value problem for fractional integrodifferential equations.…”
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Uniqueness and Existence of Solution for a System of Fractional q-Difference Equations by Wen-Xue Zhou, Hai-zhong Liu

“…Our results are based on the nonlinear alternative of Leray-Schauder type and Banach’s fixed-point theorem.…”
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Fixed Points of Multivalued G-Nonexpansive Mappings in Hadamard Spaces Endowed with Graphs by Bancha Panyanak

“…A fixed-point theorem for multivalued G-nonexpansive mappings in Hadamard spaces is proved. …”
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Existence of Positive Periodic Solutions for a Class of n-Species Competition Systems with Impulses by Peilian Guo, Yansheng Liu

“…By using the fixed point theorem on cone, some sufficient conditions are obtained on the existence of positive periodic solutions for a class of n-species competition systems with impulses. …”
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Some Existence Results for Impulsive Nonlinear Fractional Differential Equations with Closed Boundary Conditions by Hilmi Ergören, Adem Kiliçman

“…Our results are based on contracting mapping principle and Burton-Kirk fixed point theorem.…”
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Existence of Solutions for Fractional Differential Equations with p-Laplacian Operator and Integral Boundary Conditions by Jingli Xie, Lijing Duan

“…Existence of solutions is obtained by using the fixed point theorem, and an example is given to show the applicability of our main result.…”
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Positive Solutions for System of Nonlinear Fractional Differential Equations in Two Dimensions with Delay by Azizollah Babakhani

“…Our analysis relies on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone.…”
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A Remark on a Nonlocal-in-Time Heat Equation by Walker, Christoph

“…Schauder’s fixed point theorem is used to derive the existence of solutions to a semilinear heat equation. …”
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