Existence of Solutions for a Quasilinear Reaction Diffusion System by Canrong Tian

“…., activator-inhibitor mechanism). By Schauder fixed point theorem, it is shown that the system admits at least one positive solution if there exist a coupled of upper and lower solutions. …”
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Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation by Moustafa El-Shahed

“…Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.…”
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On Nonlinear Neutral Fractional Integrodifferential Inclusions with Infinite Delay by Fang Li, Ti-Jun Xiao, Hong-Kun Xu

“…A theorem about the existence of mild solutions to the fractional integrodifferential inclusions is obtained based on Martelli’s fixed point theorem. An example is given to illustrate the existence result.…”
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Positive solutions of higher order quasilinear elliptic equations by Marcelo Montenegro

“…The basic ingredients are the maximum principle, Moser iterative scheme, an eigenvalue problem, a priori estimates by rescalings, sub/supersolutions, and Krasnosel'skiĭ fixed point theorem.…”
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Some Applications of New Complex Function Space Constructed by Different Weights and Exponents by Awad A. Bakery, Elsayed A. E. Mohamed

“…Finally, we introduced an extension of Caristi’s fixed point theorem on it.…”
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Existence of Solutions of a Nonlocal Elliptic System via Galerkin Method by Alberto Cabada, Francisco Julio S. A. Corrêa

“…By means of the Galerkin method and by using a suitable version of the Brouwer fixed-point theorem, we establish the existence of at least one positive solution of a nonlocal elliptic N-dimensional system coupled with Dirichlet boundary conditions.…”
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Existence of a Short-Run Equilibrium of the Dixit-Stiglitz-Krugman Model by Minoru Tabata, Nobuoki Eshima

“…Applying the Kakutani fixed-point theorem to the set-valued operator, under the most general assumptions, we prove that the model has a short-run equilibrium.…”
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Approximate controllability for a class of fractional semilinear system with instantaneous and non-instantaneous impulses by Yunhao Chu, Yansheng Liu

“…By applying the Kuratowski measure of noncompactness and $ \rho $-set contractive fixed-point theorem, the results for the considered system were obtained. …”
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Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative by Ameth Ndiaye, Fulgence Mansal

“…Then, another result that deals with the existence of at least one solution is delivered, and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. Ulam stability of the solution is discussed before including an example to illustrate the results of the proposal.…”
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Analytical Approaches on the Attractivity of Solutions for Multiterm Fractional Functional Evolution Equations by Xiangling Li, Azmat Ullah Khan Niazi, Farva Hafeez, Reny George, Azhar Hussain

“…In this respect, we use a familiar Schauder’s fixed-point theorem (SFPT) related to the method of measure of noncompactness (MNC). …”
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Investigating a Class of Generalized Caputo-Type Fractional Integro-Differential Equations by Saeed M. Ali, Wasfi Shatanawi, Mohammed D. Kassim, Mohammed S. Abdo, S. Saleh

“…Our approach is based on Babenko’s technique, Banach’s fixed point theorem, and Banach’s space of absolutely continuous functions. …”
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Blow-Up Solutions for a Singular Nonlinear Hadamard Fractional Boundary Value Problem by Imed Bachar, Said Mesloub

“…Using properties of Green’s function and a fixed point theorem, we show that the problem has positive solutions which blow up. …”
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Upper and Lower Solutions for m-Point Impulsive BVP with One-Dimensional p-Laplacian by Junfang Zhao, Jianfeng Zhao, Weigao Ge

“…By using such techniques and the Schauder fixed point theorem, the existence of solutions and positive solutions is obtained. …”
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Fixed Point Results Satisfying Rational Type Contraction in G-Metric Spaces by Branislav Z. Popović, Muhammad Shoaib, Muhammad Sarwar

“…A unique fixed point theorem for three self-maps under rational type contractive condition is established. …”
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Positive Solutions for Third-Order p-Laplacian Functional Dynamic Equations on Time Scales by Wen Guan, Da-Bin Wang

“…By applying the Five-Functional Fixed Point Theorem, the existence criteria of three positive solutions are established.…”
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Existence and Uniqueness of Positive Solutions for Singular Nonlinear Fractional Differential Equation via Mixed Monotone Operator Method by Tian Wang, Zhaocai Hao

“…By applying the fixed point theorem in cone, we get the existence and uniqueness of positive solutions for the fractional differential equation. …”
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Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation by Yuzhen Mi

“…By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.…”
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The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order 1< α<2 by Xianghu Liu, Zhenhai Liu, Maojun Bin

“…By means of Gronwall’s inequality and Leray-Schauder’s fixed point theorem, the sufficient condition for the existence of solutions and optimal controls is presented. …”
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An Alternative Method for the Study of Impulsive Differential Equations of Fractional Orders in a Banach Space by Asma Bouzaroura, Saïd Mazouzi

“…The derived results are based on Banach's contraction theorem as well as Schaefer's fixed point theorem.…”
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The Solvability and Optimal Controls for Some Fractional Impulsive Equation by Xianghu Liu, Zhenhai Liu, Jiangfeng Han

“…Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. …”
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