Strongly exposed points in the unit ball of trace-class operators by Kourosh Nourouzi

“…A theorem of Arazy shows that every extreme point of the unit ball of trace-class operators is strongly exposed. …”
Get full text

A Numerical Algorithm for a Kirchhoff-Type Nonlinear Static Beam by Jemal Peradze

“…An approximate solution is found using the Galerkin method and the Jacobi nonlinear iteration process. A theorem on the algorithm error is proved.…”
Get full text

Ordered Variational Inequalities and Ordered Complementarity Problems in Banach Lattices by Jinlu Li, Ching-Feng Wen

“…Then we apply the Fan-KKM theorem and KKM mappings to study the solvability of these problems.…”
Get full text

Asymptotic Stability of Differential Equations with Infinite Delay by D. Piriadarshani, T. Sengadir

“…A theorem on asymptotic stability is obtained for a differential equation with an infinite delay in a function space which is suitable for the numerical computation of the solution to the infinite delay equation.…”
Get full text

First eigenvalue of submanifolds in Euclidean space by Kairen Cai

“…Then some spherical theorems and a nonimmersibility theorem of Chern and Kuiper type can be obtained.…”
Get full text

Exact boundaries of the scope of the approximate solution for a certain class of nonlinear differential equations in the complex domain by V. N. Orlov, M. V. Gasanov

“…Previously, the boundaries of the application area of the approximate solution were determined on the basis of the theorem of unique existence, but further, the obtained area was reduced due to the perturbation of the moving singular point. …”
Get full text

Certain Properties of the Modified Degenerate Gamma Function by Kwara Nantomah

“…The tools employed include Holder’s inequality, mean value theorem, Hermite–Hadamard’s inequality, and Young’s inequality. …”
Get full text

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. …”
Get full text

Positive Almost Periodic Solutions for a Time-Varying Fishing Model with Delay by Xia Li, Yongkun Li, Chunyan He

“…By means of the continuation theorem of coincidence degree theory, we prove that it has at least one positive almost periodic solution.…”
Get full text

Existence of the Mild Solutions for Delay Fractional Integrodifferential Equations with Almost Sectorial Operators by Fang Li

“…This paper is concerned with the existence of mild solutions for the fractional integrodifferential equations with finite delay and almost sectorial operators in a separable Banach space X. We obtain existence theorem for mild solutions to the above-mentioned equations, by means of measure of noncompactness and the resolvent operators associated with almost sectorial operators. …”
Get full text

Three Solutions for Inequalities Dirichlet Problem Driven by p(x)-Laplacian-Like by Zhou Qing-Mei, Ge Bin

“…Applying the version of a nonsmooth three-critical-point theorem, existence of three solutions of the problem is proved.…”
Get full text

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. …”
Get full text

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.…”
Get full text

On partitions with difference conditions by José Plínio, O. Santos, Paulo Mondek

“…We present two general theorems having interesting special cases. From one of them we give a new proof for theorems of Gordon using a bijection and from another we have a new combinatorial interpretation associated with a theorem of Göllnitz.…”
Get full text

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.…”
Get full text

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.…”
Get full text

Symmetry Transformations on the Set of Tensor Products of Rank-1 Idempotents by Yulong Tian, Jinli Xu

“…We obtain a characterization of bijective maps preserving the trace of products on the set of tensor products of rank-1 idempotents, which may be considered as a generalization of Molnár’s Wigner-type theorem in multipartite systems. The proof is based on the studies in linear preserver problems on tensor products. …”
Get full text

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. …”
Get full text

Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method by Mohammed Hirpho

“…The finite element approach was utilized in this study to solve numerically the two-dimensional time-dependent heat transfer equation coupled with the Darcy flow. The Picard-Lindelöf Theorem was used to prove the existence and uniqueness of the solution. …”
Get full text

Existence of Positive Periodic Solutions for a Class of Higher-Dimension Functional Differential Equations with Impulses by Zhang Suping, Jiang Wei

“…By employing the Krasnoselskii fixed point theorem, we establish some criteria for the existence of positive periodic solutions of a class of n-dimension periodic functional differential equations with impulses, which improve the results of the literature.…”
Get full text