| WELL-POSEDNESS STUDY FOR SOLUTIONS TO NONLINEAR DEGENERATE PARABOLIC PROBLEMS WITH VARIABLE EXPONENT | 189--200 |
Abstract
The purpose of this article is to prove the existence and uniqueness of weak solutions for nonlinear parabolic problem whose model is \begin{align*} \begin{cases} \frac{\partial v}{\partial t}-\operatorname{div}\left[|\nabla v-\Theta(v)|^{q(x)-2}(\nabla v-\Theta(v))\right]+\beta(v)=f & \text { in }\quad Q_{T}:=(0, T) \times \Omega ,\\ v=0 & \text { on }\quad \Sigma_{T}:=(0, T) \times \partial \Omega, \\ v(\cdot, 0)=v_{0} & \text { in }\quad \Omega. \end{cases} \end{align*} We transform the parabolic problem into the elliptic problem by using time discretization technique by Euler forward scheme and Rothe method combined with the theory of variable exponent Sobolev spaces.
Keywords: Nonlinear parabolic problem; existence; weak solution; variable exponent; semi-discretization; uniqueness; Rothe method.
MSC: 35K55, 35A01, 35A02
| SOME REVERSE INEQUALITIES INVOLVING TSALLIS OPERATOR ENTROPY | 201--209 |
Abstract
This paper establishes some upper and lower bounds for Tsallis operator entropy. Some applications are also given when $A$ and $B$ are bounded above and below by positive constants. We also corrected the error in the article by H. R. Moradi et al., published in 2017.
Keywords: Tsallis relative operator entropy; positive operator; relative operator entropy; geometric mean.
MSC: 47A12, 47A30, 15A60
| ON LOCAL FRACTAL FUNCTIONS OF HIGHER ORDER | 210--220 |
Abstract
In this short note we prove the existence of local fractal functions of the Orlicz-Sobolev class of order $m\geq 0.$ The graph of a local fractal function coincides with the attractor of an appropriate iterated function system, whose construction is fairly standard. Local fractal functions appear naturally as the fixed points of the Read-Bajraktarević operator when restricted to a suitable Orlicz-Sobolev space. Our results extend some of the outcomes obtained by Massopust on Lebesgue and Sobolev spaces to higher order, dimension and function spaces (where the role of the norm is now played by a Young function).
Keywords: Fractal; attractor; iterated function system (IFS); Orlicz-Sobolev space; Read-Bajraktarević operator; contractive map.
MSC: 28A80, 35J60, 37C70, 37G35, 46E30
| DENSE SET OF LARGE PERIODIC POINTS AND CHAOTIC GROUP ACTIONS | 221--226 |
Abstract
In this paper it is proved that a chaotic group action has a dense set of large periodic points. A counterexample shows that the converse doesn't hold. Furthermore, some interesting results about the topological transitivity of group actions are discussed.
Keywords: Chaotic group actions; transitivity; periodic points; periodic orbit; dense set of large periodic points.
MSC: 37B05, 37B02
| FIXED POINT RESULTS WITH RATE OF CONVERGENCE AND ERROR ESTIMATION | 227--237 |
Abstract
In this paper, we present some fixed point results metric spaces under certain admissibility conditions. A number of consequences and an illustration of the results are also discussed herein. Further, we present error estimation and rate of convergence of the fixed point iterations.
Keywords: Metric space; $(\alpha-\nu)$-dominated mapping; $(\alpha-\nu)$-regular property; $(\phi-\psi-\omega)$-generalized rational weak contraction; fixed point; error estimation; rate of convergence.
MSC: 54H10, 54H25, 47H10
| REFLEXIVITY IN WEIGHTED VECTOR-VALUED SEQUENCE SPACES | 238--248 |
Abstract
We deal with barrelledness, distinguishedness and reflexivity properties in various weighted vector-valued summable sequence spaces, with weights in the $\alpha$-dual of a perfect scalar-valued sequence space $\Lambda$. A weaker notion of distinguishedness is introduced and characterized. A nice example showing the relevance of this notion is provided.
Keywords: Summable sequence space; barrelled space; distinguished space; reflexive space; AK-space.
MSC: 46A45, 46A03, 46A25, 46A08
| MULTIPLE HOMOCLINIC SOLUTIONS FOR THE DISCRETE $p(X)$-LAPLACIAN PROBLEMS OF KIRCHHOFF TYPE | 249--262 |
Abstract
In this paper we consider the discrete anisotropic difference equation with variable exponent using critical point theory. The study of nonlinear difference equations has now attracted special attention as they have important applications in various research areas such as numerical analysis, computer science, mechanical engineering, cellular neural networks and population growth, cybernetics, etc. In many studies, the authors consider Dirichlet, Neumann or Robin type boundary conditions. However, in this paper, we consider a homoclinic boundary condition, which means that the value of the solution is equal to a constant at infinity. Here we assume that the value of the solution vanishes at infinity. In this paper, we are also interested in the existence of at least one non-trivial homoclinc solution. To achieve this, we apply firstly the direct variational method and secondly the well-known Mountain pass technique, known as the Mountain pass theorem of Ambrosetti and Rabinowitz, to obtain the existence of at least one non-trivial homoclinic solution.
Keywords: Anisotropic difference equation; critical point theory; Mountain pass lemma; direct variational method.
MSC: 39A27, 39A05, 39A14, 39A60
| DIAGONAL COMPLETION OF QUANTALE-VALUED CAUCHY TOWER SPACES | 263--276 |
Abstract
We study certain diagonal axioms defined for quantale-valued Cauchy tower spaces and their relations to similar diagonal axioms for quantale-valued convergence tower spaces and quantale-valued uniform limit tower spaces. We construct a completion for a quantale-valued Cauchy tower space that preserves a diagonal axiom and show that our construction is the coarsest possible such completion.
Keywords: Cauchy space; quantale-valued Cauchy tower space; quantale-valued metric space; quantale-valued convergence tower space; diagonal axioms; completeness; completion.
MSC: 54E15, 54A20, 54A40, 54D35
| OPEN-LOCATING DOMINATING NUMBER FOR FLOWER SNARKS | 277--282 |
Abstract
The problem of finding an open-locating dominating set is a variant of the domination problem where both domination and the ability to identify a certain vertex are required. The cardinality of such a dominating set is called the open-locating dominating number. The open-locating domination problem has been proven to be NP-hard in the general case. In this paper, the exact value of the old domination number is provided for the class of Flower snark graphs.
Keywords: Open-locating dominating set; graphs; Flower snarks.
MSC: 05C69, 05C07