Two Positive Solutions of Third-Order BVP with Integral Boundary Condition and Sign-Changing Green's Function by Bing-Wei Niu, Jian-Ping Sun, Qiu-Yan Ren

“…Although the corresponding Green's function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions on f by using the two-fixed-point theorem due to Avery and Henderson. An example is also included to illustrate the main results obtained.…”
Get full text

The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions by Wenjie Ma, Yujun Cui

“…By using the Guo-Krasnoselskii’s fixed point theorem on cone and the properties of the Green’s function, some new results on the existence and nonexistence of positive solutions for the fractional differential equation are obtained.…”
Get full text

Existence of Solution and Self-Exciting Attractor in the Fractional-Order Gyrostat Dynamical System by Muhammad Marwan, Gauhar Ali, Ramla Khan

“…This work identifies the influence of chaos theory on fractional calculus by providing a theorem for the existence and stability of solution in fractional-order gyrostat model with the help of a fixed-point theorem. We modified an integer order gyrostat model consisting of three rotors into fractional order by attaching rotatory fuel-filled tank and provided an iterative scheme for our proposed model as a working rule of obtained analytical results. …”
Get full text

Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales by Jian Liu, Fuyi Xu

“…We obtain the existence of three positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.…”
Get full text

Remarks on Some Recent Fixed Point Results on Quaternion-Valued Metric Spaces by Ravi P. Agarwal, Hamed H. Alsulami, Erdal Karapınar, Farshid Khojasteh

“…Very recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. …”
Get full text

Coincidence Point Results on Relation Theoretic Fw,Rg-Contractions and Applications by Muhammad Aslam, Hassen Aydi, Samina Batul, Amna Naz

“…Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for Fw,Rg-contractions in metric spaces equipped with a transitive binary relation. …”
Get full text

Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions by Jian Chang, Jian-Ping Sun, Ya-Hong Zhao

“…Under some suitable conditions, by applying a fixed point theorem due to Avery and Peterson, we obtain the existence of multiple positive solutions to the above problem. …”
Get full text

Existence of Bounded Positive Solutions for Partial Difference Equations with Delays by Zeqing Liu, Zhihua Wu, Young Chel Kwun, Shin Min Kang

“…With the help of the Banach fixed-point theorem, the existence results of uncountably many bounded positive solutions for the partial difference equation are given; some Mann iterative schemes with errors are suggested, and the error estimates between the iterative schemes and the bounded positive solutions are discussed. …”
Get full text

Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order by J. Caballero, J. Harjani, K. Sadarangani

“…Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also given to illustrate the results.…”
Get full text

Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian by Imed Bachar, Habib Mâagli, Said Mesloub

“…Our method is based on the global estimates of potential functions and the Schauder fixed point theorem.…”
Get full text

Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems by S. Nageswara Rao, M. Zico Meetei

“…Values of the parameters λ and μ are determined for which boundary value problem has positive solution by utilizing a fixed point theorem on cone.…”
Get full text

Existence of Three Positive Solutions for m-Point Discrete Boundary Value Problems with p-Laplacian by Yanping Guo, Wenying Wei, Yuerong Chen

“…We consider the multi-point discrete boundary value problem with one-dimensional p-Laplacian operator Δ(ϕp(Δu(t−1))+q(t)f(t,u(t),Δu(t))=0, t∈{1,…,n−1} subject to the boundary conditions: u(0)=0, u(n)=∑i=1m−2aiu(ξi), where ϕp(s)=|s|p−2s,p>1,ξi∈{2,…,n−2} with 1<ξ1<⋯<ξm−2<n−1 and ai∈(0,1),0<∑i=1m−2ai<1. Using a new fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.…”
Get full text

Positive Solutions for Some Competitive Fractional Systems in Bounded Domains by Imed Bachar, Habib Mâagli, Noureddine Zeddini

“…Using some potential theory tools and the Schauder fixed point theorem, we prove the existence and precise global behavior of positive continuous solutions for the competitive fractional system (−Δ|D)α/2u+p(x)uσvr=0, (−Δ|D)α/2v+q(x)usvβ=0 in a bounded C1,1-domain D in ℝn (n≥3), subject to some Dirichlet conditions, where 0<α<2, σ,β≥1,s,r≥0. …”
Get full text

Null Controllability of a Four Stage and Age-Structured Population Dynamics Model by Amidou Traoré, Bedr’Eddine Ainseba, Oumar Traoré

“…Our method combines fixed point theorem and Carleman estimate. We end this work with numerical illustrations.…”
Get full text

Existence and Uniqueness of Solutions for Fractional Boundary Value Problems under Mild Lipschitz Condition by Imed Bachar, Habib Mâagli, Hassan Eltayeb

“…Based on the Banach fixed point theorem on an appropriate space, we prove that this problem possesses a unique continuous solution u satisfying ut≤cωt,for t∈0,1 and c>0, where ωt≔tα−21−t2.…”
Get full text

Existence of Solutions for Boundary Value Problem of a Caputo Fractional Difference Equation by Zhiping Liu, Shugui Kang, Huiqin Chen, Jianmin Guo, Yaqiong Cui, Caixia Guo

“…We use Schauder fixed point theorem to deduce the existence of solutions. …”
Get full text

Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations by Yige Zhao, Shurong Sun, Zhenlai Han, Qiuping Li

“…By the properties of the Green function and Guo-Krasnosel'skii fixed point theorem on cones, the eigenvalue intervals of the nonlinear fractional differential equation boundary value problem are considered, some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established. …”
Get full text

Existence of Some Semilinear Nonlocal Functional Differential Equations of Neutral Type by Hsiang Liu, Cheng-Wen Liao, Chin-Tzong Pang

“…We first employ the Schauder fixed-point theorem to prove the existence of solution on the interval for that is small enough, and, then, by letting and using a diagonal argument, we have the existence results on the interval . …”
Get full text

Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras by Madjid Eshaghi Gordji, Badrkhan Alizadeh, Young Whan Lee, Gwang Hui Kim

“…We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.…”
Get full text

Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument by Xuemei Zhang, Meiqiang Feng

“…Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. …”
Get full text