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.…”
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On Katugampola Fourier Transform by Tariq O. Salim, Atta A. K. Abu Hany, Mohammed S. El-Khatib

“…The inversion formula and the convolution theorem for the Katugampola Fourier transform are considered.…”
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Iterates of Volterra operators and indeterminate forms by Pablo Braz e Silva, Andrés R. R. Papa

“…We state and prove a theorem showing how iterates of the Volterra operator can be used to evaluate indeterminate forms of type 0/0. …”
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Soft intersection almost bi-quasi-interior ideals of semigroups by Aslıhan Sezgin, Zeynep BAŞ, Aleyna İlgin

“…With this vital theorem, several interesting relationships between certain types of almost BQI-ideals of semigroups, such as minimal, prime, semiprime, and strongly prime almost BQI-ideals and certain types of soft intersection almost BQI-ideals, are derived.  …”
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Evaluation of Dynamic Compaction Load Conversion Methods and Vibration Reduction Treatments by Jixuan Li, Wenli Wang, Longping Luo, Xiaoliang Yao, Jiangang Hu

“…Subsequently, the momentum theorem method was utilized to investigate the influence of depth and distance of vibration isolation trench, as well as the properties of vibration isolation materials on vibration reduction effect. …”
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Isomorphism of generalized triangular matrix-rings and recovery of tiles by R. Khazal, S. Dăscălescu, L. Van Wyk

“…We prove an isomorphism theorem for generalized triangular matrix-rings, over rings having only the idempotents 0and 1, in particular, over indecomposable commutative rings or over local rings (not necessarily commutative). …”
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Inscribing closed non-σ-lower porous sets into Suslin non-σ-lower porous sets by Luděk Zajíček, Miroslav Zelený

“…In fact, we prove a general result of this type on “abstract porosities.” This general theorem is also applied to ball small sets in Hilbert spaces and to σ-cone-supported sets in separable Banach spaces.…”
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On the existence of bounded solutions of nonlinear elliptic systems by Abdelaziz Ahammou

“…We are concerned with the existence of a negative subsolution and a nonnegative supersolution in the sense of Hernandez; then we construct some compact operator T and some invariant set K where we can use the Leray Schauder's theorem.…”
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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. …”
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Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications by Jiang Zhu, Dongmei Liu

“…By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.…”
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Finite-Time Lyapunov Functions and Impulsive Control Design by Huijuan Li, Qingxia Ma

“…A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. …”
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Discrimination in a General Algebraic Setting by Benjamin Fine, Anthony Gaglione, Seymour Lipschutz, Dennis Spellman

“…As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.…”
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Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach by Panos K. Palamides, Alex P. Palamides

“…Our technique relies on the continuum property (connectedness and compactness) of the solutions funnel (Kneser's Theorem), combined with the corresponding vector field.…”
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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.…”
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Modeling and Mathematical Analysis of Labor Force Evolution by Sanaa ElFadily, Abdelilah Kaddar

“…The mathematical analysis of our model focuses on the local behavior of the labor force around a positive equilibrium position; the existence of a branch of periodic solutions bifurcated from the positive equilibrium is then analyzed according to the Hopf bifurcation theorem. Finally, we performed numerical simulations to illustrate our theoretical results.…”
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Bifurcation of the equivariant minimal interfaces in a hydromechanics problem by A. Y. Borisovich, W. Marzantowicz

“…We show that a symmetry of the base of tube let us to apply a method developed earlier by the first author and based on the Crandall-Rabinowitz bifurcation theorem. Using the natural symmetry of the corresponding variational problem defined by a symmetry of region and restricting the functional to spaces of invariant functions we show the existence of bifurcation, and describe its local picture, for interfaces parametrized by the square and disc.…”
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Noncompact Perturbation of Sweeping Process with Delay in Banach Spaces by F. Aladsani, A. G. Ibrahim

“…This work extends some recent existence theorems concerning sweeping processes from Hilbert spaces setting to Banach spaces setting. …”
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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. …”
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Nonstationary Fronts in the Singularly Perturbed Power-Society Model by M. G. Dmitriev, A. A. Pavlov, A. P. Petrov

“…The interpretations of the solutions to the equation are presented in terms of applied model. The possibility theorem for the problem of getting the solution having some preassigned properties by means of parametric control is proved.…”
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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. …”
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