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Wyświetlanie 1-15 z 37
Tytuł:
Recovering a part of potential by partial information on spectra of boundary problems
Autorzy:
Pivovarchik, V.
Powiązania:
https://bibliotekanauki.pl/articles/255115.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
sine-type function
Lagrange interpolation series
Dirichlet boundary value problem
Dirichlet-Neumann boundary value problem
Opis:
Under additional conditions uniqueness of the solution is proved for the following problem. Given 1) the spectrum of the Dirichlet problem for the Sturm-Liouville equation on [0, a] with real potential q(x) mem L2(0, a), 2) a certain part of the spectrum of the Dirichlet problem for the same equation on [a/3, a] and 3) the potential on [0, a/3]. The aim is to find the potential on [a/3 ,a].
Źródło:
Opuscula Mathematica; 2005, 25, 1; 131-137
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
One boundary value problem including a spectral parameter in all boundary conditions
Autorzy:
Kabataş, Ayşe
Powiązania:
https://bibliotekanauki.pl/articles/29519516.pdf
Data publikacji:
2023
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
boundary value problems
asymptotics
Green’s functions
Opis:
In this paper, asymptotic formulae for solutions and Green’s function of a boundary value problem are investigated when the equation and the boundary conditions contain a spectral parameter.
Źródło:
Opuscula Mathematica; 2023, 43, 5; 651-661
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positive solutions to a third order nonlocal boundary value problem with a parameter
Autorzy:
Szajnowska, Gabriela
Zima, Mirosława
Powiązania:
https://bibliotekanauki.pl/articles/29519483.pdf
Data publikacji:
2024
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
boundary value problem
nonlocal boundary conditions
positive solution
cone
Opis:
We present some sufficient conditions for the existence of positive solutions to a third order differential equation subject to nonlocal boundary conditions. Our approach is based on the Krasnosel’skiĭ-Guo fixed point theorem in cones and the properties of the Green’s function corresponding to the BVP under study. The main results are illustrated by suitable examples.
Źródło:
Opuscula Mathematica; 2024, 44, 2; 267-283
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The numerical solution of nonlinear two-point boundary value problems using iterated deferred correction - a survey
Autorzy:
Cash, J. R.
Powiązania:
https://bibliotekanauki.pl/articles/255625.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
deferred correction
boundary value problems
conditioning
mesh selection
Opis:
The use of iterated deferred correction has proved to be a very efficient approach to the numerical solution of general first order systems of nonlinear two-point boundary value problems. In particular the two high order codes TWPBVP.f, based on mono-implicit Runge-Kutta (MIRK) formulae, and TWPBVPL.f based on Lobatto Runge-Kutta formulae as well as the continuation codes ACDC.f and COLMOD.f are now widely used. In this survey we describe some of the problems involved in the derivation of efficient deferred correction schemes. In particular we consider the construction of high order methods which preserve the stability of the underlying formulae, the choice of the mesh choosing algorithm which is based both on local accuracy and conditioning, and the computation of continuous solutions.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 269-287
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the dependence on parameters for second order discrete boundary value problems with the p(k)-Laplacian
Autorzy:
Smejda, J.
Wieteska, R.
Powiązania:
https://bibliotekanauki.pl/articles/952772.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
discrete boundary value problems
variational methods
mountain pass theorem
Opis:
In this paper we study the existence and the nonexistence of solutions for the boundary value problems of a class of nonlinear second-order discrete equations depending on a parameter. Variational (the mountain pass technique) and non-variational methods are applied.
Źródło:
Opuscula Mathematica; 2014, 34, 4; 851-870
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The use of integral information in the solution of a two-point boundary value problem
Autorzy:
Drwięga, T.
Powiązania:
https://bibliotekanauki.pl/articles/255474.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
boundary value problem
complexity
worst case setting
linear information
Opis:
We study the worst-case ε-complexity of a two-point boundary value problem u″(x) = ƒ(x) u (x), x ∈ [0,T], u(0) = c, u′ (T) = 0, where c,T ∈ R (c ≠ 0, T > 0) and ƒ is a nonnegative function with r (r ≥ 0) continuous bounded derivatives. We prove an upper bound on the complexity for linear information showing that a speed-up by two orders of magnitude can be obtained compared to standard information. We define an algorithm based on integral information and analyze its error, which provides an upper bound on the ε-complexity.
Źródło:
Opuscula Mathematica; 2007, 27, 2; 205-220
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monotone iterative technique for fractional differential equations with periodic boundary conditions
Autorzy:
Ramirez, J. D.
Vatsala, A. S.
Powiązania:
https://bibliotekanauki.pl/articles/255247.pdf
Data publikacji:
2009
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Riemann-Liouville fractional derivative
monotone method
periodic boundary value problem
Opis:
In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.
Źródło:
Opuscula Mathematica; 2009, 29, 3; 289-304
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A general boundary value problem and its Weyl function
Autorzy:
Ryzhov, V.
Powiązania:
https://bibliotekanauki.pl/articles/255861.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
abstract boundary value problem
symmetric operators
Green formula
Weyl function
Opis:
We study the abstract boundary value problem defined in terms of the Green identity and introduce the concept of Weyl operator function M(·) that agrees with other definitions found in the current literature. In typical cases of problems arising from the multidimensional partial equations of mathematical physics the function M(·) takes values in the set of unbounded densely defined operators acting on the auxiliary boundary space. Exact formulae are obtained and essential properties of M(·) are studied. In particular, we consider boundary problems defined by various boundary conditions and justify the well known procedure that reduces such problems to the "equation on the boundary" involving the Weyl function, prove an analogue of the Borg-Levinson theorem, and link our results to the classical theory of extensions of symmetric operators.
Źródło:
Opuscula Mathematica; 2007, 27, 2; 305-331
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The d-bar formalism for the modified Veselov-Novikov equation on the half-plane
Autorzy:
Hwang, Guenbo
Moon, Byungsoo
Powiązania:
https://bibliotekanauki.pl/articles/2048897.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
initial-boundary value
integrable nonlinear PDE
spectral analysis
d-bar
Opis:
We study the modified Veselov–Novikov equation (mVN) posed on the half-plane via the Fokas method, considered as an extension of the inverse scattering transform for boundary value problems. The mVN equation is one of the most natural (2+1)-dimensional generalization of the (1+1)-dimensional modified Korteweg-de Vries equation in the sense as to how the Novikov–Veselov equation is related to the Korteweg–de Vries equation. In this paper, by means of the Fokas method, we present the so-called global relation for the mVN equation, which is an algebraic equation coupled with the spectral functions, and the d-bar formalism, also known as Pompieu’s formula. In addition, we characterize the d-bar derivatives and the relevant jumps across certain domains of the complex plane in terms of the spectral functions.
Źródło:
Opuscula Mathematica; 2022, 42, 2; 179-217
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multiple solutions for systems of multi-point boundary value problems
Autorzy:
Graef, J. R.
Heidarkhani, S.
Kong, L.
Powiązania:
https://bibliotekanauki.pl/articles/255713.pdf
Data publikacji:
2013
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
multiple solutions
multi-point boundary value problem
critical point theory
Opis:
In this paper, we establish the existence of at least three solutions of the multi-point boundary value system [formula]. The approaches used are based on variational methods and critical point theory.
Źródło:
Opuscula Mathematica; 2013, 33, 2; 293-306
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and uniqueness results for fractional differential equations with boundary value conditions
Autorzy:
Lv, L.
Wang, J.
Wei, W.
Powiązania:
https://bibliotekanauki.pl/articles/254863.pdf
Data publikacji:
2011
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fractional differential equations
boundary value conditions
singular Gronwall inequality
existence
uniqueness
Opis:
In this paper, we study the existence and uniqueness of fractional differential equations with boundary value conditions. A new generalized singular type Gronwall inequality is given to obtain important a priori bounds. Existence and uniqueness results of solutions are established by virtue of fractional calculus and fixed point method under some weak conditions. An example is given to illustrate the results.
Źródło:
Opuscula Mathematica; 2011, 31, 4; 629-643
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations
Autorzy:
Auzinger, W.
Karner, E.
Koch, O.
Weinmuller, E.
Powiązania:
https://bibliotekanauki.pl/articles/255635.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
polynomial collocation
singular boundary value problems
linear and nonlinear eigenvalue problems
Opis:
We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.
Źródło:
Opuscula Mathematica; 2006, 26, 2; 229-241
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fundamental solution of the problem describing ship motion in waves
Autorzy:
Jankowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/255889.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
ship hydrodynamics
boundary value problem
free-surface potential flows
fundamental solution
Opis:
The problem describing a ship motion in waves comprises the Laplace equation, boundary condition on wetted surface of the ship, condition on the free surface of the sea in the form of a differential equation, the radiation condition, and a condition at infinity. This problem can be transformed to a Fredholm equation of second kind, and then numerically solved using the boundary element method, if the fundamental solution of the problem is known. This paper presents the derivation of the fundamental solution. In physical interpretation, the fundamental solution represents the moving and pulsating source under free surface of the sea. The free surface elevation, generated by the source for different forward speed and frequency of pulsation, is presented in this paper.
Źródło:
Opuscula Mathematica; 2006, 26, 3; 471-481
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on a fourth order discrete boundary value problem
Autorzy:
Galewski, M.
Smejda, J.
Powiązania:
https://bibliotekanauki.pl/articles/255355.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
discrete boundary value problem
variational method
coercivity
continuous dependence on paremeters
Opis:
Using variational methods we investigate the existence of solutions and their dependence on parameters for certain fourth order difference equations.
Źródło:
Opuscula Mathematica; 2012, 32, 1; 115-123
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Right focal boundary value problems for difference equations
Autorzy:
Henderson, J.
Liu, X.
Lyons, J. W.
Neugebauer, J. T.
Powiązania:
https://bibliotekanauki.pl/articles/255580.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
difference equation
boundary value problem
right focal
fixed point theorem
positive solution
Opis:
An application is made of a new Avery et al. fixed point theorem of compression and expansion functional type in the spirit of the original fixed point work of Leggett and Williams, to obtain positive solutions of the second order right focal discrete boundary value problem. In the application of the fixed point theorem, neither the entire lower nor entire upper boundary is required to be mapped inward or outward. A nontrivial example is also provided.
Źródło:
Opuscula Mathematica; 2010, 30, 4; 447-456
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 37

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