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.…”
Get full text

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. …”
Get full text

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.…”
Get full text

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. …”
Get full text

Global Exponential Stability of Positive Pseudo-Almost-Periodic Solutions for a Model of Hematopoiesis by Junxia Meng

“…Under suitable assumptions, and by using fixed point theorem, sufficient conditions are given to ensure that all solutions of this model converge exponentially to the positive pseudo almost periodic solution for the considered model. …”
Get full text

Existence of Solution via Integral Inequality of Volterra-Fredholm Neutral Functional Integrodifferential Equations with Infinite Delay by Kishor D. Kucche, Machindra B. Dhakne

“…To obtain a priori bounds of solutions required in Krasnoselski-Schaefer type fixed point theorem, we have used an integral inequality established by B. …”
Get full text

Almost Automorphic Mild Solutions to Neutral Parabolic Nonautonomous Evolution Equations with Nondense Domain by Zhanrong Hu, Zhen Jin

“…Combining the exponential dichotomy of evolution family, composition theorems for almost automorphic functions with Banach fixed point theorem, we establish new existence and uniqueness theorems for almost automorphic mild solutions to neutral parabolic nonautonomous evolution equations with nondense domain. …”
Get full text

Periodic Solutions and Exponential Stability of a Class of Neural Networks with Time-Varying Delays by Yingxin Guo, Mingzhi Xue

“…Employing fixed point theorem, we make a further investigation of a class of neural networks with delays in this paper. …”
Get full text

Existence of Solutions for a Class of Coupled Fractional Differential Systems with Nonlocal Boundary Conditions by Tingting Qi, Yansheng Liu, Yujun Cui

“…Applying Schauder fixed point theorem and Leray-Schauder nonlinear alternative theory, this paper is concerned with the existence of solutions to coupled fractional differential systems with fractional integral boundary value conditions. …”
Get full text

Existence of Traveling Waves for a Delayed SIRS Epidemic Diffusion Model with Saturation Incidence Rate by Kai Zhou, Qi-Ru Wang

“…By using the cross-iteration method and Schauder’s fixed point theorem, we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions. …”
Get full text

Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity by Yongqing Wang, Lishan Liu, Yonghong Wu

“…We first derive some properties of the associated Green function and then obtain some results on the existence of positive solutions by means of the Krasnoselskii's fixed point theorem in a cone.…”
Get full text

Class 𝔄-KKM(X,Y,Z), General KKM Type Theorems, and Their Applications in Topological Vector Space by Gusheng Tang, Qingbang Zhang

“…As applications, Ky Fan’s matching theorem and Fan-Browder fixed-point theorem are extended, and some existence theorems of solutions for the generalized vector equilibrium problems are established under noncompact setting, which improve and generalize some known results.…”
Get full text

Existence and H-U Stability of Solution for Coupled System of Fractional-Order with Integral Conditions Involving Caputo-Hadamard Derivatives, Hadamard Integrals by Muath Awadalla, Muthaian Subramanian, Murugesan Manigandan, Kinda Abuasbeh

“…We employ adequate conditions to achieve existence and uniqueness results for the presented problems by utilizing the Banach contraction principle and the Leray-Schauder fixed point theorem. We also show Ulam-Hyers stability using the standard functional analysis technique. …”
Get full text

Local existence result of the single dopant diffusion including cluster reactions of high order by R. Bader, W. Merz

“…The local existence result is based on the fixed point theorem of Schauder.…”
Get full text

Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative by Changyou Wang, Haiqiang Zhang, Shu Wang

“…By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigated. …”
Get full text

Triple Positive Solutions of a Nonlocal Boundary Value Problem for Singular Differential Equations with p-Laplacian by Jufang Wang, Changlong Yu, Yanping Guo

“…We establish the existence of triple positive solutions of an m-point boundary value problem for the nonlinear singular second-order differential equations of mixed type with a p-Laplacian operator by Leggett-William fixed point theorem. At last, we give an example to demonstrate the use of the main result of this paper. …”
Get full text

On the Existence of Three Positive Solutions for a Caputo Fractional Difference Equation by Lili Kong, Huiqin Chen, Luping Li, Shugui Kang

“…In this paper, we introduce the application of three fixed point theorem by discussing the existence of three positive solutions for a class of Caputo fractional difference equation boundary value problem. …”
Get full text

Positive Solutions for Sturm-Liouville Boundary Value Problems in a Banach Space by Hua Su, Lishan Liu, Yonghong Wu

“…The sufficient condition for the existence of positive solution is obtained by the fixed point theorem of strict set contraction operators in the frame of the ODE technique. …”
Get full text

Mean-Square Almost Periodic Solutions for Impulsive Stochastic Host-Macroparasite Equation on Time Scales by Pan Wang, Qingmei Lin, Yongkun Li

“…By use of the Banach fixed point theorem and Gronwall-Bellman’s inequality technique on time scales, we obtain the existence and exponential stability of mean-square almost periodic solutions for the host-macroparasite equation on time scales. …”
Get full text

Nonemptiness and Compactness of Solutions Set for Nondifferentiable Multiobjective Optimization Problems by Xin-kun Wu, Jia-wei Chen, Yun-zhi Zou

“…Nonemptiness and compactness of the solutions set for the nondifferentiable multiobjective optimization problems are proved by using the FKKM theorem and a fixed-point theorem.…”
Get full text