scholarly journals The Existence of Solutions to the NonhomogeneousA-Harmonic Equations with Variable Exponent

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Haiyu Wen
Keyword(s):  
Weak Solution ◽  
Sobolev Space ◽  
Existence And Uniqueness ◽  
Obstacle Problem ◽  
Variable Exponent ◽  
Existence Of Solutions ◽  
Variable Exponent Sobolev Space ◽  
Harmonic Equation ◽  
Weighted Variable

We first discuss the existence and uniqueness of weak solution for the obstacle problem of the nonhomogeneousA-harmonic equation with variable exponent, and then we obtain the existence of the solutions of the equationd⋆A(x,dω)=B(x,dω)in the weighted variable exponent Sobolev spaceWdp(x)(Ω,Λl,μ).

scholarly journals Three solutions to a p(x)-Laplacian problem in weighted-variable-exponent Sobolev space

2013 ◽  
Vol 21 (2) ◽  
pp. 195-205 ◽  
Author(s):  
Wen-Wu Pan ◽  
Ghasem Alizadeh Afrouzi ◽  
Lin Li
Keyword(s):  
Sobolev Space ◽  
Neumann Problem ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Variable Exponent ◽  
Three Solutions ◽  
Variable Exponent Sobolev Space ◽  
Weighted Variable

Abstract In this paper, we verify that a general p(x)-Laplacian Neumann problem has at least three weak solutions, which generalizes the corresponding result of the reference [R. A. Mashiyev, Three Solutions to a Neumann Problem for Elliptic Equations with Variable Exponent, Arab. J. Sci. Eng. 36 (2011) 1559-1567].

Quasilinear parabolic problem with variable exponent: Qualitative analysis and stabilization

2018 ◽  
Vol 20 (08) ◽  
pp. 1750065 ◽  
Author(s):  
Jacques Giacomoni ◽  
Vicenţiu Rădulescu ◽  
Guillaume Warnault
Keyword(s):  
Weak Solution ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Variable Exponent ◽  
Global Behavior ◽  
Variable Exponents ◽  
Nonlinear Parabolic ◽  
Quasilinear Parabolic Problem ◽  
Quasilinear Elliptic ◽  
Quasilinear Parabolic

We discuss the existence and uniqueness of the weak solution of the following nonlinear parabolic problem: [Formula: see text] which involves a quasilinear elliptic operator of Leray–Lions type with variable exponents. Next, we discuss the global behavior of solutions and in particular the convergence to a stationary solution as [Formula: see text].

scholarly journals On a Class of Anisotropic Nonlinear Elliptic Equations with Variable Exponent

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Guoqing Zhang ◽  
Hongtao Zhang
Keyword(s):  
Weak Solution ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Priori Estimates

Based on truncation technique and priori estimates, we prove the existence and uniqueness of weak solution for a class of anisotropic nonlinear elliptic equations with variable exponentp(x)→growth. Furthermore, we also obtain that the weak solution is locally bounded and regular; that is, the weak solution isLloc∞(Ω)andC1,α(Ω).

scholarly journals On compact and bounded embedding in variable exponent Sobolev spaces and its applications

2019 ◽  
Vol 9 (2) ◽  
pp. 401-414
Author(s):  
Farman Mamedov ◽  
Sayali Mammadli ◽  
Yashar Shukurov
Keyword(s):  
Sobolev Space ◽  
Growth Condition ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Lebesgue Spaces ◽  
Nonstandard Growth ◽  
Variable Exponent Sobolev Spaces ◽  
Nonstandard Growth Condition ◽  
Nonlinear Ode ◽  
Weighted Variable

Abstract For a weighted variable exponent Sobolev space, the compact and bounded embedding results are proved. For that, new boundedness and compact action properties are established for Hardy’s operator and its conjugate in weighted variable exponent Lebesgue spaces. Furthermore, the obtained results are applied to the existence of positive eigenfunctions for a concrete class of nonlinear ode with nonstandard growth condition.

scholarly journals Characterization of the variable exponent Sobolev norm without derivatives

2017 ◽  
Vol 19 (03) ◽  
pp. 1650022 ◽  
Author(s):  
Peter Hästö ◽  
Ana Margarida Ribeiro
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Sobolev Norm ◽  
Difference Quotient ◽  
Variable Exponent Sobolev Space ◽  
The Difference ◽  
Fractional Smoothness

The norm in classical Sobolev spaces can be expressed as a difference quotient. This expression can be used to generalize the space to the fractional smoothness case. Since the difference quotient is based on shifting the function, it cannot be generalized to the variable exponent case. In its place, we introduce a smoothed difference quotient and show that it can be used to characterize the variable exponent Sobolev space.

scholarly journals Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1431
Author(s):  
Bilal Basti ◽  
Nacereddine Hammami ◽  
Imadeddine Berrabah ◽  
Farid Nouioua ◽  
Rabah Djemiat ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Biological Models ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Single Form ◽  
Stability Results

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

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