Search results for: BOUNDARY CONDITIONS INVOLVING STIELTJES INTEGRALS
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Successive Iterative Method for Higher-Order Fractional Differential Equations Involving Stieltjes Integral Boundary Conditions
PublicationIn this paper, the existence of positive solutions to fractional differential equations with delayed arguments and Stieltjes integral boundary conditions is discussed. The convergence of successive iterative method of solving such problems is investigated. This allows us to improve some recent works. Some numerical examples illustrate the results.
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Monotone iterative method to second order differential equations with deviating arguments involving Stieltjes integral boundary conditions
PublicationWe use a monotone iterative method for second order differential equations with deviating arguments and boundary conditions involving Stieltjes integrals. We establish sufficient conditions which guarantee that such problems have extremal solutions in the corresponding region bounded by lower and upper solutions. We also discuss the situation when problems have coupled quasi-solutions. We illustrate our results by three examples.
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First-order differential equations with nonlocal boundary conditions
PublicationWe study a first-order boundary value problem subject to some boundary conditions given by Riemann-Stieltjes integrals. Using a monotone iterative method, we formulate sufficient conditions which guarantee the existence of extremal or quasi-solutions in the corresponding region bounded by upper and lower solutions of our problems. The case when a unique solution exists is also investigated. Some examples are given to illustrate...
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublicationWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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Monotone iterative method for first-order differential equations at resonance
PublicationThis paper concerns the application of the monotone iterative technique for first-order differential equations involving Stieltjes integrals conditions. We discuss such problems at resonance when the measure in the Stieltjes integral is positive and also when this measure changes the sign. Sufficient conditions which guarantee the existence of extremal, unique and quasi-solutions are given. Three examples illustrate the results.
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublicationIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Path integrals formulations leading to propagator evaluation for coupled linear physics in large geometric models
PublicationReformulating linear physics using second kind Fredholm equations is very standard practice. One of the straightforward consequences is that the resulting integrals can be expanded (when the Neumann expansion converges) and probabilized, leading to path statistics and Monte Carlo estimations. An essential feature of these algorithms is that they also allow to estimate propagators for all types of sources, including initial conditions....
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Positive solutions for second order impulsive differential equations involving Stieltjes integral conditions
PublicationIn this paper we investigate integral boundary value problems for fourth order differentialequations with deviating arguments.Wediscuss our problem both for advanced or delayedarguments. We establish sufficient conditions under which such problems have positivesolutions. To obtain the existence of multiple (at least three) positive solutions, we use afixed point theorem due to Avery and Peterson. An example is also included to...
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Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (-1,1)
PublicationZaprezentowano metode obliczenia dwóch całek oznaczonych zawierających wielomiany Gegenbauera. Wynik wykorzystano do znalezienia sum czterech szeregów o wyrazach zawierających wielomiany Gegenbauera oraz funkcje Legendre'a (pierwszego lub drugiego rodzaju) na odcinku (-1,1).
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On Dynamic Boundary Conditions Within the Linear Steigmann-Ogden Model of Surface Elasticity and Strain Gradient Elasticity
PublicationWithin the strain gradient elasticity we discuss the dynamic boundary conditions taking into account surface stresses described by the Steigmann–Ogden model. The variational approach is applied with the use of the least action functional. The functional is represented as a sum of surface and volume integrals. The surface strain and kinetic energy densities are introduced. The Toupin–Mindlin formulation of the strain gradient elasticity...
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On Non-holonomic Boundary Conditions within the Nonlinear Cosserat Continuum
PublicationWithin the framework of the nonlinear micropolar elastic continuum we discuss non-holonomic kinematic boundary conditions. By non-holonomic boundary conditions we mean linear relations between virtual displacements and virtual rotations given on the boundary. Such boundary conditions can be used for modelling of complex material interactions in the vicinity of the boundaries and interfaces.
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The literature review on boundary conditions of use for non-residential buildings
PublicationThis paper describes the results of qualitative and quantitative literature reviews on boundary conditions within educational buildings, emphasising the users' perspective. The reviews were performed before and during the COVID-19 pandemic using Scopus, Taylor& Francis, Web of Science databases. The boundary conditions understood as special characteristics for use and or precondition, determining specific features of buildings...
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Model Order Reduction for Problems With Dispersive Surface Boundary Conditions
PublicationThis letter proposes a new scheme for reduced-order finite-element modeling of electromagnetic structures with nonlinear, dispersive surface boundary conditions, which optimally exploits the numerically stable and efficient MOR framework for second-order systems provided by SAPOR method. The presented results of numerical experiments for an example of a waveguide filter demonstrate the superior accuracy of the resulting reduced models...
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Thermal boundary conditions to simulate friction layers and coatings at sliding contacts
PublicationA brief review of the thermal boundary conditions specified at sliding interfaces was performed. New thermal boundary conditions were derived aimed at solving problems of sliding with account of surface layers representing friction layers and tribological coatings. Based on the assumption of linear temperature distributions in the surface layers, the proposed conditions enable one to simplify simulations by eliminating the surface...
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The literature review on boundary conditions of use for non-residential buildings. Educational buildings.
PublicationThis paper describes the results of qualitative and quantitative literature reviews on boundary conditions within educational buildings, emphasising the users' perspective. The studies were performed before and during the COVID-19 pandemic using Scopus, Taylor& Francis, and Web of Science databases. The boundary conditions are understood as special characteristics for use and or precondition, determining specific features of...
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Absorbing Boundary Conditions Derived Based on Pauli Matrices Algebra
PublicationIn this letter, we demonstrate that a set of absorbing boundary conditions (ABCs) for numerical simulations of waves, proposed originally by Engquist and Majda and later generalized by Trefethen and Halpern, can alternatively be derived with the use of Pauli matrices algebra. Hence a novel approach to the derivation of one-way wave equations in electromagnetics is proposed. That is, the classical wave equation can be factorized...
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Positive solutions to Sturm–Liouville problems with non-local boundary conditions
PublicationIn this paper, the existence of at least three non-negative solutions to non-local boundary-value problems for second-order differential equations with deviating arguments α and ζ is investigated. Sufficient conditions, which guarantee the existence of positive solutions, are obtained using the Avery–Peterson theorem. We discuss our problem for both advanced and delayed arguments. An example is added to illustrate the results.
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Impact of Boundary Conditions on Acoustic Excitation of EntropyPerturbations in a Bounded Volume of Newtonian Gas
PublicationExcitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoreticallyconsidered in this work. The dynamic equation for an excess density which specifies the entropy mode,has been obtained by means of the method of projections. It takes the form of the diffusion equation withan acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient isproportional...
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Boundary conditions for non-residential buildings from the user’s perspective: literature review
PublicationBackground and objective: This paper aims to review the boundary conditions (B/C) in specific categories (energy, building use, and lighting) within non-residential buildings to pave the way to a better understanding of users’ requirements and needs of the built environment. For this paper, B/C are understood as unique preconditions, specific characteristics for use, determining specific features of buildings, enabling an accurate...
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Differential equations with integral boundary conditions
PublicationStosuje się metodę iteracji monotonicznych opartą na dolnym i górnym rozwiązaniu. Przy jednostronnym warunku Lipschitza uzyskano pewne wyniki dotyczące rozwiązań zwyczajnych równań różniczkowych z całkowym warunkiem brzegowym. Sformułowano warunki dostateczne na istnienie jedynego rozwiązania (lub rozwiązań ekstremalnych) w pewnym segmencie. Podano przykłady ilustrujące przyjęte założenia.