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1
Content available Pseudo-differential equations and conical potentials: 2-dimensional case
Vasilyev Vladimir B.
Opuscula Mathematica
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2019
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Vol. 39, no. 1
109--124
EN
We consider two-dimensional elliptic pseudo-differential equation in a plane sector. Using a special representation for an elliptic symbol and the formula for a general solution we study the Dirichlet problem for such equation. This problem was reduced to a system of linear integral equations and then after some transformations to a system of linear algebraic equations. The unique solvability for the Dirichlet problem was proved in Sobolev-Slobodetskii spaces and a priori estimate for the solution is given.
2
On some nonlinear hyperbolic p(x,t)-Laplacian equations
Ahmedatt T., Touzani A., Aberqi A., Yazough C.
Journal of Applied Analysis
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2018
|
Vol. 24, nr 1
55--69
EN
This paper is devoted to study the global existence of solutions of the hyperbolic Dirichlet equation Utt=Lu+f(x,t) in ΩT=Ω×(0,T), where L is a nonlinear operator and ϕ(x,t,⋅), f(x,t) and the exponents of the nonlinearities p(x,t) and μ(x,t) are given functions.
3
Content available Positive solutions with specific asymptotic behavior for a polyharmonic problem on Rn
Dhifli A.
Opuscula Mathematica
|
2015
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Vol. 35, no. 1
5--19
EN
This paper is concerned with positive solutions of the semilinear polyharmonic equation [formula] on Rn, where m and n are positive integers with n > 2m, α ∈ e (—1,1). The coefncient a is assumed to satisfy[formula], where Λ ∈ (2m,∞) and [formula]is positive with [formula], one also assumes that [formula]. We prove the existence of a positive solution u such that [formula], with [formula] and a function L, given explicitly in terms of L and satisfying the same condition as infinity. (Given positive functions ∫ and g on Rn, ∫≈ g means that [formula]for some constant c > 1.)
4
Content available Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus
Dridi S., Khamessi B.
Opuscula Mathematica
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2015
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Vol. 35, no. 1
21--36
EN
In this paper, we establish existence and asymptotic behavior of a positive clas­sical solution to the following semilinear boundary value problem: [formula] Here O is an annulus in [formula] and q is a positive function in [formula], satisfying some appropriate assumptions related to Karamata regular variation theory. Our arguments combine a method of sub- and supersolutions with Karamata regular variation theory.
5
Content available Positivity preserving results for a biharmonic equation under Dirichlet boundary conditions
Omrane H. B., Khenissy S.
Opuscula Mathematica
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2014
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Vol. 34, no. 3
601--608
EN
We prove a dichotomy result giving the positivity preserving property for a biharmonic equation with Dirichlet boundary conditions arising in MEMS models. We adapt some ideas in [H.-Ch. Grunau, G. Sweers, Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions, Math. Ann. 307 (1997), 589–626].
6
Content available Numerical Implementation of the Fictitious Domain Method for Elliptic Equations
Temirbekov A. N., Wójcik W.
International Journal of Electronics and Telecommunications
|
2014
|
Vol. 60, No. 3
219-223
EN
In this paper, we consider an elliptic equation with strongly varying coefficients. Interest in the study of these equations is connected with the fact that this type of equation is obtained when using the fictitious domain method. In this paper, we propose a special method for the numerical solution of elliptic equations with strongly varying coefficients. A theorem is proved for the rate of convergence of the iterative process developed. A computational algorithm and numerical calculations are developed to illustrate the effectiveness of the proposed method.
7
Content available remote Existence and uniqueness of solutions of the dirichlet nonlocal problem with nonlocal initial condition
Byszewski L., Winiarska T.
Czasopismo Techniczne. Nauki Podstawowe
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2014
|
R. 111, z. 2-NP
3--7
EN
The aim of this paper is to prove the existence and uniqueness of solutions of the Dirichlet nonlocal problem with nonlocal initial condition. The considerations are extensions of results by E. Andreu-Vaillo, J. M. Mazón, J. D. Rossi and J. J. Toledo-Melero.
PL
W artykule udowodniono istnienie i jednoznaczność rozwiązań nielokalnego zagadnienia Dirichleta z nielokalnym warunkiem początkowym. Rozważania są rozszerzeniami rezultatów otrzymanych przez E. Andreu-Vaillo, J. M. Mazóna, J. D. Rossi i J. J. Toledo-Melero.
8
Content available On a boundary value problem for the system of partial differential equations describing non-simple thermoelasticity
Kołakowski H., Łazuka J.
Biuletyn Wojskowej Akademii Technicznej
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2014
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Vol. 63, nr 2
171-176
PL
W pracy rozważamy zagadnienie Dirichleta dla równań teorii termosprężystości materiałów złożonych. Pokazaliśmy, że zagadnienie to generuje operator fredholmowski działający pomiędzy odpowiednimi przestrzeniami Sobolewa.
EN
In this paper we study the Dirichlet problem for the system of equations describing non-simple thermoelasticity. Using the general theory of the elliptic problem we show that this problem is elliptic one.
9
Content available remote Three Solutions Theorem for a Quasilinear Dirichlet Boundary Value Problem
Goncerz P.
Schedae Informaticae
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2012
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Vol. 21
159--168
EN
We consider a Dirichlet boundary value problem driven by the p-Laplacian with the right hand side being a Carathéodory function. The existence of solutions is obtained by the use of a special form of the three critical points theorem.
10
Content available remote Solution of plane Dirichlet problem using compactly supported 2D wavelet scaling functions
Katunin A.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 1
31-40
EN
The paper presents the solution of the homogeneous plane Dirichlet problem using the wavelet-Galerkin method with various 2D compactly supported wavelet scaling functions. An analysis of approximation accuracy was performed with respect to the orders of investigated wavelet scaling functions and the level of approximation. The most effective scaling functions for solving the Dirichlet problem were indicated and discussed.
11
Content available remote Existence of bounded solutions for fourth order Dirichlet problems with convex-concave nonlinearity
Galewski M.
Demonstratio Mathematica
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2009
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Vol. 42, nr 1
75-81
EN
We consider the Dirichlet boundary value problem for higher order O. D. E. with nonlinearity being the sum of a derivative of a convex and of a concave function in case when no growth condition is imposed on the concave part.
12
Content available Existence of solutions of the Dirichlet problem for an infinite system of nonlinear differential-functional equations of elliptic type
Zabawa T.S.
Opuscula Mathematica
|
2005
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Vol. 25, no. 2
333-343
EN
The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin's method of lower and uper functions.
13
Content available remote On-sided estimates for quasimonotone systems of boundary value problem
Herzog G.
Demonstratio Mathematica
|
2004
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Vol. 37, nr 4
847--856
EN
We prove existence and uniqueness theorems for Dirichlet boundary value problems of the form u" + f(t,u) = 0, u(0) = uo, u(1) = ui in ordered finite dimensional Banach spaces, involving one-sided estimates and quasimonotonicity.
14
Content available remote Hemivariational inequalities governed by the p-Laplacian -Dirichlet problem
Naniewicz Z.
Control and Cybernetics
|
2004
|
Vol. 33, no 2
181-210
EN
A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition (Naniewicz, 1994). The existence of solutions for problems with Dirichlet boundary conditions is established by making use of Chang's version of the critical point theory for non-smooth locally Lipschitz functionals (Chang, 1981), combined with the Galerkin method. A class of problems with nonlinear potentials fulfilling the classical growth hypothesis without Ainbrosetti-Rabinowitz type assumption is discussed. The approach is based on the recession technique introduced in Naniewicz (2003).
15
Content available remote Dirichlet problems with variable boundary data for nonlinear partial differential equations
Bors D.
Demonstratio Mathematica
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2000
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Vol. 33, nr 2
295-312
EN
In this paper we consider some systems of partial differential equations with variable boundary data. Some sufficient conditions under which solutions of these systems continuously depend on boundary data are given. The proofs of the main result of this work are based on some variational methods.
16
Content available remote The Dirichlet problem for biharmonic equation in case the half plane
Lupu M.
Demonstratio Mathematica
|
1999
|
Vol. 32, nr 1
41-53
EN
Using the representations of the solution of Dirichlet problem for the half plane, the basic biharmonic problem (BP) is solved. Applying the half plane theorem on Almansi type representation of the solution is given by direct or analytical methods. New formulas are proved and for special cases some applications are presented.
17
Content available remote The semicoercive case of the Dirichlet problem of even order
Sidorczyk M.
Demonstratio Mathematica
|
1998
|
Vol. 31, nr 3
615-625
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