Yazar "Aydin, Ismail" seçeneğine göre listele

Listeleniyor 1 - 20 / 26
  • [ X ]
    Öğe
    Almost all weak solutions of the weighted p(.)-biharmonic problem
    (Springernature, 2024) Aydin, Ismail
    We give a new compact embedding theorem, and use an equivalent norm to obtain some different solutions of the weighted p(.)-biharmonic eigenvalue problem [GRAPHICS] Using Mountain Pass Theorem we show that the problem has a nontrivial weak solution. Moreover, we obtain infinite many pairs of solutions of the problem due to the Fountain Theorem.
  • [ X ]
    Öğe
    APPROXIMATION OF AN OPTIMAL BV-CONTROL PROBLEM IN THE COEFFICIENT FOR THE p(x)-LAPLACE EQUATION
    (Oles Honchar Dnipro National University, 2024) Aydin, Ismail; Kogut, Peter
    We study a Dirichlet optimal control problem for a quasilinear monotone elliptic equation with the so-called weighted p(x)-Laplace operator. The coefficient of the p(x)-Laplacian, the weight u, we take as a control in BV (Ω) ∩ L∞(Ω). In this article, we use box-type constraints for the admissible controls. In order to handle the inherent degeneracy of the p(x)-Laplacian, we use a special two-parametric regularization scheme. We derive existence and uniqueness of variational V -solutions to the underlying boundary value problem and the corresponding optimal control problem. Further we discuss the asymptotic behaviour of the solutions to regularized problems on each (ε, k)-level as the parameters tend to zero and infinity, respectively. The characteristic feature of the considered OCP is the fact that the exponent p(x) is assumed to be Lebesgue-measurable, and we do not impose any additional assumptions on p(x) like to be a Lipschitz function or satisfy the so-called log-Hölder continuity condition. © I. Aydin, P. Kogut, 2024.
  • [ X ]
    Öğe
    Compact embeddings of weighted variable exponent Sobolev spaces and existence of solutions for weighted p(•)-Laplacian
    (Taylor & Francis Ltd, 2021) Unal, Cihan; Aydin, Ismail
    In this study, we define double weighted variable exponent Sobolev spaces W-1,W-q(.),W-p(.) (Omega, theta(0),theta) with respect to two different weight functions. Also, we investigate the basic properties of this spaces. Moreover, we discuss the existence of weak solutions for weighted Dirichlet problem of p(center dot)-Laplacian equation -div(theta(x) vertical bar del f vertical bar p(x)(-2)del f) = theta(0)(x) vertical bar f vertical bar(q(x)-2) f x is an element of Omega f = 0 x is an element of partial derivative Omega under some conditions of compact embedding involving the double weighted variable exponent Sobolev spaces.
  • [ X ]
    Öğe
    COMPACT EMBEDDINGS ON A SUBSPACE OF WEIGHTED VARIABLE EXPONENT SOBOLEV SPACES
    (Springer Basel Ag, 2019) Unal, Cihan; Aydin, Ismail
    In this paper, we define an intersection space between weighted classical Lebesgue spaces and weighted Sobolev spaces with variable exponent. We consider the basic properties of the space. Also, we investigate some inclusions, continuous embeddings, and compact embeddings under some conditions.
  • [ X ]
    Öğe
    DIRICHLET TYPE PROBLEM WITH P(.)-TRIHARMONIC OPERATOR
    (Editura Bibliotheca-Bibliotheca Publ House, 2021) Aydin, Ismail
    In this study, we consider the existence of multiple weak solutions to a class of Dirichlet type problem involving p(.)-triharmonic {-Delta(3)(p(.))u = lambda vertical bar u vertical bar(q(.)-2)u in Omega, u = Delta u = Delta(2)u = 0 on partial derivative Omega, under some suitable conditions.
  • [ X ]
    Öğe
    Existence and multiplicity of weak solutions for eigenvalue Robin problem with weighted p(.)-Laplacian
    (Springer-Verlag Italia Srl, 2023) Aydin, Ismail; Unal, Cihan
    By applying Mountain Pass Lemma, Ekeland's variational principle and Fountain Theorem, we prove the existence and multiplicity of solutions for the following Robin problem {-div(a(x) vertical bar del u vertical bar(p(x)-2) del u) =lambda b(x)vertical bar u vertical bar(q(x)-2) u, x is an element of Omega a(x) vertical bar del u vertical bar(p(x)-2) partial derivative u/partial derivative u + beta(x)vertical bar u vertical bar(p(x)-2) u = 0, x is an element of partial derivative Omega, under some appropriate conditions in the space W-a,b(1, p(.)) (Omega).
  • [ X ]
    Öğe
    EXISTENCE AND UNIQUENESS OF A WEAK SOLUTION FOR SINGULAR WEIGHTED ROBIN PROBLEM INVOLVING p ( . )- BIHARMONIC OPERATOR
    (Ankara Univ, Fac Sci, 2024) Aydin, Ismail
    The aim of this paper is to find the existence of solutions for the following class of singular fourth order equation involving the weighted p ( . )- biharmonic operator: { ( triangle a ( x ) triangle u p ( x ) - 2 triangle u = lambda b ( x ) u q ( x ) - 2 u + V ( x ) u - gamma ( x ) , x is an element of ohm ,
  • [ X ]
    Öğe
    Existence of Weak Solutions for Weighted Robin Problem Involving p(.)-biharmonic operator
    (Springer India, 2024) Kulak, Oznur; Aydin, Ismail; Unal, Cihan
    Using Mountain Pass Theorem, we consider the existence of weak solutions of weighted Robin problem involving p(.)-biharmonic operator { a(x)Delta(2)(p(x)) u = lambda b(x)vertical bar u vertical bar(q(x)-2)u, in Omega a(x)vertical bar Delta u vertical bar(p(x)-2)partial derivative u/partial derivative v + beta(x) vertical bar u vertical bar(p(x)-2) u = 0, on partial derivative Omega under some conditions in the space W-a,b(2,p(.)) (Omega).
  • [ X ]
    Öğe
    INVERSE CONTINUOUS WAVELET TRANSFORM IN WEIGHTED VARIABLE EXPONENT AMALGAM SPACES
    (Ankara Univ, Fac Sci, 2020) Kulak, Oznur; Aydin, Ismail
    The wavelet transform is an useful mathematical tool. It is a mapping of a time signal to the time-scale joint representation. The wavelet transform is generated from a wavelet function by dilation and translation. This wavelet function satisfies an admissible condition so that the original signal can be reconstructed by the inverse wavelet transform. In this study, we firstly give some basic properties of the weighted variable exponent amalgam spaces. Then we investigate the convergence of the theta-means of f in these spaces under some conditions. Finally, using these results the convergence of the inverse continuous wavelet transform is considered in these spaces.
  • [ X ]
    Öğe
    On a subalgebra of Lw1(G)
    (Univ Babes-Bolyai, 2012) Aydin, Ismail
    Let G be a locally compact abelian group with Haar measure. We define the spaces B-1,B-w (p, q) = L-w(1)(G) boolean AND (L-p, l(q)) (G) and discuss some properties of these spaces. We show that B-1,B-w (p, q) is an S-w(G) space. Furthermore we investigate compact embeddings and the multipliers of B-1,B-w (p, q).
  • [ X ]
    Öğe
    On some properties of the spaces Awp(x)(R n)
    (2009) Aydin, Ismail; Gürkanli, A. Turan
    For 1 ≤ p < ∞, Ap (Rn) denotes the space of all complex-valued functions in L1 (Rn) whose Fourier transforms f̌ belong to Lp(Rn). A number of authors such as Larsen, Liu and Wang [12], Martin and Yap [14], Lai [11] worked on this space. Some generalizations to the weighted case was given by Gurkanli [7], Feichtinger and Gurkanli [4], Fischer, Gurkanli and Liu [5]. In the present paper we give another generalization of Ap (Rn) to the generalized Lebesgue space Lp(x)(Rn). We define A p(x)w (Rn) to be the space of all complex-valued functions in L1w (Rn) whose Fourier transforms f̌ belong to the generalized Lebesgue space L p(x)(Rn). We endow it with a sum norm and show that A p(x)w (Rn) is an Sw(Rn) space [2]. Further we discuss the multipliers of Ap(x)w (Rn).
  • [ X ]
    Öğe
    On the weighted variable exponent amalgam space W (Lp(x), Lmq)
    (Elsevier, 2014) Gürkanli, A. Turan; Aydin, Ismail
    In [4], a new family. W (Lp(x),Lmq) of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space Lp(x) (ℝ) and the global component is a weighted Lebesgue space Lqm(ℝ). This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality. W (Lp(x),Lmq)=Lq(ℝ). Later we give some characterization of Wiener amalgam space. W (Lp(x),Lmq). In Section 3 we define the Wiener amalgam space. W (FLp(x),Lmq) and investigate some properties of this space, where. FLp(x) is the image of Lp(x) under the Fourier transform. In Section 4, we discuss boundedness of the Hardy-Littlewood maximal operator between some Wiener amalgam spaces. © 2014 Wuhan Institute of Physics and Mathematics.
  • [ X ]
    Öğe
    ON THE WEIGHTED VARIABLE EXPONENT AMALGAM SPACE W(Lp(x) , Lmq)
    (Springer, 2014) Gurkanli, A. Turan; Aydin, Ismail
    In [4], a new family W(L-p(x), L-m(q))of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space L-p(x) (R) and the global component is a weighted Lebesgue space L-m(q) (R). This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality W (L-p(x), L-m(q)) = L-q (R). Later we give some characterization of Wiener amalgam space W (L-p(x), L-m(q)). In Section 3 we define the Wiener amalgam space W (FLp(x), L-m(q)) and investigate some properties of this space, where FLp(x) is the image of L-p(x)) under the Fourier transform. In Section 4, we discuss boundedness of the Hardy-Littlewood maximal operator between some Wiener amalgam spaces.
  • [ X ]
    Öğe
    ON VECTOR-VALUED CLASSICAL AND VARIABLE EXPONENT AMALGAM SPACES
    (Ankara Univ, Fac Sci, 2017) Aydin, Ismail
    Let 1 <= p, q, s <= infinity and 1 <= r(.) <= infinity, where r(.) is a variable exponent. In this paper, we introduce firstly vector-valued variable exponent amalgam spaces (L-r(.) (R, E), l(s)). Secondly, we investigate some basic properties of (L-r(.) (R, E), l(s)) spaces. Finally, we recall vector-valued classical amalgam spaces (L-p (G, A), l(q)), and inquire the space of multipliers from (L-p1 (G, A), l(q1)) to (L-p2' (G, A*), l(q2)')
  • [ X ]
    Öğe
    Some properties of thinness and fine topology with relative capacity
    (Springer-Verlag Italia Srl, 2023) Unal, Cihan; Aydin, Ismail
    In this paper, we introduce a thinness in sense to a type of relative capacity for weighted variable exponent Sobolev space. Moreover, we reveal some properties of this thinness and consider the relationship with finely open and finely closed sets. We discuss fine topology and compare this topology with Euclidean one. Finally, we give some information about importance of the fine topology in the potential theory.
  • [ X ]
    Öğe
    Some results on a weighted convolution Algebra
    (Jangjeon Research Institute for Mathematical Sciences and Physics, 2015) Ünal, Cihan; Aydin, Ismail
    In this paper, we define Ap(.)ω1,ω (ℝn) to be the space of all complex-valued functions in Lω1(ℝn) whose Fourier transforms f belong to the weighted variable exponent Lebesgue space Lυp (ℝn). Also, we investigate some inclusions and compact embeddings properties and further discuss multipliers of this spaces.
  • [ X ]
    Öğe
    THE INCLUSION THEOREMS FOR GENERALIZED VARIABLE EXPONENT GRAND LEBESGUE SPACES
    (Kangwon-Kyungki Mathematical Soc, 2021) Aydin, Ismail; Unal, Cihan
    In this paper, we discuss and investigate the existence of the inclusion L-p(.),L-theta (mu) subset of L-q(.),L-theta (nu), where mu and nu are two finite measures on (X, Sigma) Moreover, we show that the generalized variable exponent grand Lebesgue space L-p(.),L-theta (Omega) has a potential-type approximate identity, where Omega is a bounded open subset of R-d.
  • [ X ]
    Öğe
    The Kolmogorov-Riesz theorem and some compactness criterions of bounded subsets in weighted variable exponent amalgam and Sobolev spaces
    (Springer-Verlag Italia Srl, 2020) Aydin, Ismail; Unal, Cihan
    We study totally bounded subsets in weighted variable exponent amalgam and Sobolev spaces. Moreover, this paper includes several detailed generalized results of some compactness criterions in these spaces.
  • [ X ]
    Öğe
    The Riesz capacity in variable exponent Lebesgue spaces
    (Academic Publications Ltd., 2017) Ünal, Cihan; Aydin, Ismail
    In this paper, we study a capacity theory based on a definition of a Riesz potential in the Euclidean space. Also, we define the Riesz (α, p(.))- capacity and discuss the properties of the capacity in the variable exponent Lebesgue space Lp(.)(ℝn). © 2017 Academic Publications.
  • [ X ]
    Öğe
    THREE SOLUTIONS TO A STEKLOV PROBLEM INVOLVING THE WEIGHTED p(.)-LAPLACIAN
    (Rocky Mt Math Consortium, 2021) Aydin, Ismail; Unal, Cihan
    We study a nonlinear Steklov boundary-value problem involving the weighted p(.)-Laplacian. Using the Ricceri's variational principle, we obtain the existence of at least three weak solutions in double weighted variable exponent Sobolev space.