Continuity of solutions for the Δ ϕ -Laplacian operator

2020 ◽  
pp. 1-28
Author(s):  
Natalí A. Cantizano ◽  
Ariel M. Salort ◽  
Juan F. Spedaletti
Keyword(s):  
General Class ◽  
Sufficient Conditions ◽  
Laplacian Operator ◽  
Growth Type ◽  
Nonstandard Growth ◽  
Continuity Of Solutions ◽  
Domain Perturbations

In this paper we give sufficient conditions to obtain continuity results of solutions for the so called ϕ-Laplacian Δ ϕ with respect to domain perturbations. We point out that this kind of results can be extended to a more general class of operators including, for instance, nonlocal nonstandard growth type operators.

Asymptotic behavior of repeated eigenvalues of perturbed self-adjoint elliptic operators

2021 ◽  
pp. 1-16
Author(s):  
Alexander Dabrowski
Keyword(s):  
General Type ◽  
Differential Operators ◽  
Laplacian Operator ◽  
Variational Characterization ◽  
Repeated Eigenvalues ◽  
Direct Extension ◽  
Asymptotic Formulae ◽  
Elliptic Differential Operators ◽  
Domain Perturbations ◽  
Boundary Deformation

A variational characterization for the shift of eigenvalues caused by a general type of perturbation is derived for second order self-adjoint elliptic differential operators. This result allows the direct extension of asymptotic formulae from simple eigenvalues to repeated ones. Some examples of particular interest are presented theoretically and numerically for the Laplacian operator for the following domain perturbations: excision of a small hole, local change of conductivity, small boundary deformation.

scholarly journals Poisson distribution series on a general class of analytic functions

2020 ◽  
Vol 24 (2) ◽  
pp. 241-251
Author(s):  
Basem A. Frasin
Keyword(s):  
Integral Operator ◽  
Poisson Distribution ◽  
Analytic Functions ◽  
General Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Class A ◽  
Poisson Distribution Series ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for the Poisson distribution series to be in a general class of analytic functions with negative coefficients. Further, we consider an integral operator related to the Poisson distribution series to be in this class. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

scholarly journals Impulsive Fractional Differential Equations with p-Laplacian Operator in Banach Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jingjing Tan ◽  
Kemei Zhang ◽  
Meixia Li
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Laplacian Operator ◽  
Multiple Point ◽  
Noncompactness Measure ◽  
Fractional Differential ◽  
Sadovskii Fixed Point Theorem

In this paper, we study a class of boundary value problem (BVP) with multiple point boundary conditions of impulsive p-Laplacian operator fractional differential equations. We establish the sufficient conditions for the existence of solutions in Banach spaces. Our analysis relies on the Kuratowski noncompactness measure and the Sadovskii fixed point theorem. An example is given to demonstrate the main results.

scholarly journals Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yanke Du ◽  
Yanlu Li ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Periodic Orbits ◽  
General Class ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Multiple Equilibrium ◽  
Activation Functions ◽  
Discontinuous Activation ◽  
Discontinuous Activation Functions ◽  
Multiple Equilibrium Points

A general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and locally exponential stability of multiple equilibrium points and periodic orbits, which ensure thatn-dimensional Cohen-Grossberg neural networks withk-level discontinuous activation functions can haveknequilibrium points orknperiodic orbits. Finally, several examples are given to illustrate the feasibility of the obtained results.

Mathematical models for nonlocal elastic composite materials

2017 ◽  
Vol 6 (4) ◽  
pp. 355-382 ◽  
Author(s):  
Giuseppina Autuori ◽  
Federico Cluni ◽  
Vittorio Gusella ◽  
Patrizia Pucci
Keyword(s):  
Composite Materials ◽  
Nonlocal Elasticity ◽  
Fractional Laplacian ◽  
Numerical Estimate ◽  
Sufficient Conditions ◽  
Elastic Behavior ◽  
Laplacian Operator ◽  
Elastic Rod ◽  
Central Difference ◽  
Dimension One

AbstractIn this paper we derive and solve nonlocal elasticity a model describing the elastic behavior of composite materials, involving the fractional Laplacian operator. In dimension one we consider in (($\mathcal{D}$)) the case of a nonlocal elastic rod restrained at the ends, and we completely solve the problem showing the existence of a unique weak solution and providing natural sufficient conditions under which this solution is actually a classical solution of the problem. For the model (($\mathcal{D}$)) we also perform numerical simulations and a parametric analysis, in order to highlight the response of the rod, in terms of displacements and strains, according to different values of the mechanical characteristics of the material. The main novelty of this approach is the extension of the central difference method by the numerical estimate of the fractional Laplacian operator through a finite-difference quadrature technique. For higher dimensions {N\geq 2} we study more general problems for which the existence of weak solutions is proved via variational methods. The obtained results provide an original contribute in the knowledge of composite materials with properties of nonlocal elasticity.

scholarly journals On the Periodicity of General Class of Difference Equations

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 75 ◽  
Author(s):  
Osama Moaaz ◽  
Hamida Mahjoub ◽  
Ali Muhib
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
General Class ◽  
Sufficient Conditions ◽  
Usual Method ◽  
Necessary And Sufficient Conditions ◽  
New Method ◽  
Nonlinear Difference Equations ◽  
Existence Of Periodic Solutions ◽  
Necessary And Sufficient

In this paper, we are interested in studying the periodic behavior of solutions of nonlinear difference equations. We used a new method to find the necessary and sufficient conditions for the existence of periodic solutions. Through examples, we compare the results of this method with the usual method.

scholarly journals A fractional q-difference equation eigenvalue problem with p(t)-Laplacian operator

2021 ◽  
Vol 26 (3) ◽  
pp. 482-501
Author(s):  
Chengbo Zhai ◽  
Jing Ren
Keyword(s):  
Difference Equation ◽  
Fixed Point Theorems ◽  
Iterative Scheme ◽  
Laplacian Operator ◽  
Stieltjes Integral ◽  
Unique Positive Solution ◽  
Nonstandard Growth ◽  
Nonhomogeneous Boundary ◽  
Constant Growth ◽  
Theoretical Results

This article is devoted to studying a nonhomogeneous boundary value problem involving Stieltjes integral for a more general form of the fractional q-difference equation with p(t)-Laplacian operator. Here p(t)-Laplacian operator is nonstandard growth, which has been used more widely than the constant growth operator. By using fixed point theorems of  φ – (h, e)-concave operators some conditions, which guarantee the existence of a unique positive solution, are derived. Moreover, we can construct an iterative scheme to approximate the unique solution. At last, two examples are given to illustrate the validity of our theoretical results.

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