arXiv subjects

Cihan Unal

Publications and source records attributed to Cihan Unal.

11 recordsLinked to original sources

arXiv2020

On some general multiplying solutions results of a Robin problem

By applying Ricceri's variational principle, we demonstrate the existence of solutions for the following Robin problem \begin{equation*}\left\{ \begin{array}{cc}-\func{div}\left( \omega _{1}(x)\left\vert \nabla u\right\vert^{p(x)-2}\nabla u\right) =\lambda \omega _{2}(x)f(x,u), & x\in \Omega \\ \omega _{1}(x)\left\vert \nabla u\right\vert ^{p(x)-2}\frac{\partial u}{ \partial \upsilon }+\beta (x)\left\vert u\right\vert ^{p(x)-2}u=0, & x\in \partial \Omega , \end{array} \right. \end{equation*} in $W_{\omega _{1},\omega _{2}}^{1,p(.)}\left( \Omega \right) $ under some appropriate conditions.

math.AP↗

arXiv2020

Some new weighted compact embeddings results and existence of weak solutions for eigenvalue Robin problem

By applying Mountain Pass Lemma, Ekeland's and Ricceri's variational principle, Fountain Theorem, we prove the existence and multiplicity of solutions for the following Robin problem \begin{equation*} \left\{ \begin{array}{cc} -\text{div}\left( a(x)\left\vert \nabla u\right\vert ^{p(x)-2}\nabla u\right) =\lambda b(x)\left\vert u\right\vert ^{q(x)-2}u, & x\in \Omega \\ a(x)\left\vert \nabla u\right\vert ^{p(x)-2}\frac{\partial u}{\partial \upsilon }+\beta (x)\left\vert u\right\vert ^{p(x)-2}u=0, & x\in \partial \Omega , \end{array} \right. \end{equation*} under some appropriate conditions in the space $W_{a,b}^{1,p(.)}\left( \Omega \right).$

math.AP↗

arXiv2020

Three solutions to a Steklov problem involving the weighted p(.)-Laplacian

This paper is concerned with a nonlinear Steklov boundary-value problem involving 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.

math.AP↗

arXiv2019

Inclusion theorems for grand Lorentz spaces

In this paper, we consider some inclusion theorems for grand Lorentz spaces $L^{p,q)}\left( X,\mu \right) $ and $\Lambda _{p),\omega }$ where $\mu $ is a finite measure on $\left( X,\Sigma \right) .$ Moreover, we consider the problem of the convergence of approximate identities in these spaces.

math.FA↗

arXiv2019

Ergodic Theorem in Grand Variable Exponent Lebesgue Spaces

We consider several fundamental properties of grand variable exponent Lebesgue spaces. Moreover, we discuss Ergodic theorems in these spaces whenever the exponent is invariant under the transformation.

math.FA↗

arXiv2019

The Banach Algebra of Functions With Fourier Transforms in Weighted Amalgam Spaces

In this paper, we define $A_{\vartheta _{1},\vartheta _{2}}^{p,1,q,r}\left(G\right) $ to be space of all functions in $\left( L_{\vartheta_{1}}^{p},\ell ^{1}\right) $ whose Fourier transforms belong to $\left( L_{\vartheta _{2}}^{q},\ell ^{r}\right) .$ Moreover, we consider the basic and advance properties of this space including Banach algebra, translation invariant, Banach module, a generalized type of Segal algebra etc. Also, we study some inclusions, compact embeddings in sense to weights and further discuss multipliers of this space.

math.FA↗

arXiv2019

Some Properties of Thinness and Fine Topology with Relative Capacity

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.

math.FA↗

arXiv2019

On some properties of relative capacity and thinness in weighted variable exponent Sobolev spaces

In this paper, we define weighted relative $p(.)$-capacity and discuss properties of capacity in the space $W_{\vartheta }^{1,p(.)}(\mathbb{R}^{n}).$ Also, we investigate some properties of weighted variable Sobolev capacity. It is shown that there is a relation between these two capacities. Moreover, we introduce a thinness in sense to this new defined relative capacity and prove an equivalence statement for this thinness.

math.FA↗

arXiv2019

The Kolmogorov-Riesz Theorem and Some Compactness Criterions of Bounded Subsets in Weighted Variable Exponent Amalgam and Sobolev Spaces

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.

math.FA↗

arXiv2019

Existence of Weak Solutions for $p(.)$-Laplacian Equation via Compact Embeddings of the Double Weighted Variable Exponent Sobolev Spaces

In this study, we define double weighted variable exponent Sobolev spaces $W^{1,q(.),p(.)}\left( \Omega ,\vartheta _{0},\vartheta \right) $ 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 $p(.)$-Laplacian equation \begin{equation*} \left\{ \begin{array}{cc} -\text{div}\left( \vartheta (x)\left\vert \nabla f\right\vert ^{p(x)-2}\nabla f\right) =\vartheta _{0}(x)\left\vert f\right\vert ^{q(x)-2}f & x\in \Omega \\ f=0 & x\in \partial \Omega \end{array} \right. \end{equation*} under some conditions of compact embedding involving the double weighted variable exponent Sobolev spaces.

math.AP↗

arXiv2019

Weighted Stochastic Field Exponent Sobolev Spaces and Nonlinear Degenerated Elliptic Problem

In this study, we consider weighted stochastic field exponent function spaces $L_{\vartheta }^{p(.,.)}\left( D\times \Omega \right) $ and $W_{\vartheta }^{k,p(.,.)}\left( D\times \Omega \right) $. Also, we investigate some basic properties and embeddings of these spaces. Finally, we present an application of these spaces to the stochastic partial differential equations with stochastic field growth.

math.FA↗