scholarly journals On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Mohaemd Jleli ◽  
Bessem Samet
Keyword(s):  
Critical Exponent ◽  
Weak Solutions ◽  
Fractional Derivatives ◽  
Sobolev Type ◽  
Existence And Nonexistence

We consider two fractional in time nonlinear Sobolev-type inequalities involving potential terms, where the fractional derivatives are defined in the sense of Caputo. For both problems, we study the existence and nonexistence of nontrivial local weak solutions. Namely, we show that there exists a critical exponent according to which we have existence or nonexistence.

scholarly journals Positive solutions for a system of fractional differential equations with p-Laplacian operator and multi-point boundary conditions

2018 ◽  
Vol 23 (5) ◽  
pp. 771-801 ◽  
Author(s):  
Rodica Luca
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Existence Results ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Existence And Nonexistence ◽  
Fractional Differential

>We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann–Liouville fractional differential equations with parameters and p-Laplacian operator subject to multi-point boundary conditions, which contain fractional derivatives. The proof of our main existence results is based on the Guo–Krasnosel'skii fixed-point theorem.

scholarly journals Multiple of Solutions for Nonlocal Elliptic Equations with Critical Exponent Driven by the Fractional p-Laplacian of Order s

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
M. Khiddi
Keyword(s):  
Variational Methods ◽  
Critical Exponent ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Nehari Manifold ◽  
Lusternik Schnirelmann ◽  
The Nehari Manifold

In this paper, we study the existence of infinitely many weak solutions for nonlocal elliptic equations with critical exponent driven by the fractional p-Laplacian of order s. We show the above result when λ>0 is small enough. We achieve our goal by making use of variational methods, more specifically, the Nehari Manifold and Lusternik-Schnirelmann theory.

scholarly journals Regularities of Time-Fractional Derivatives of Semigroups Related to Schrodinger Operators with Application to Hardy-Sobolev Spaces on Heisenberg Groups

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Zhiyong Wang ◽  
Chuanhong Sun ◽  
Pengtao Li
Keyword(s):  
Sobolev Spaces ◽  
Equivalence Relation ◽  
Fractional Derivatives ◽  
Sobolev Type ◽  
Square Function ◽  
Heisenberg Groups ◽  
Square Functions ◽  
Regularity Properties ◽  
Reverse Hölder ◽  
Derivatives Of

In this paper, assume that L=−Δℍn+V is a Schrödinger operator on the Heisenberg group ℍn, where the nonnegative potential V belongs to the reverse Hölder class BQ/2. By the aid of the subordinate formula, we investigate the regularity properties of the time-fractional derivatives of semigroups e−tLt>0 and e−tLt>0, respectively. As applications, using fractional square functions, we characterize the Hardy-Sobolev type space HL1,αℍn associated with L. Moreover, the fractional square function characterizations indicate an equivalence relation of two classes of Hardy-Sobolev spaces related with L.

On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type

2021 ◽  
Vol 85 (1) ◽  
Author(s):  
Maxim Olegovich Korpusov ◽  
Alexander Anatolyevich Panin ◽  
Andrey Evgenievich Shishkov
Keyword(s):  
Cauchy Problem ◽  
Critical Exponent ◽  
Model Equation ◽  
Blow Up ◽  
Sobolev Type ◽  
The Cauchy Problem

Dynamics of a Fractional Derivative Type of a Viscoelastic Rod With Random Excitation

2015 ◽  
Vol 18 (5) ◽  
Author(s):  
Teodor Atanacković ◽  
Marko Nedeljkov ◽  
Stevan Pilipović ◽  
Danijela Rajter-Ćiri
Keyword(s):  
Fractional Derivative ◽  
Weak Solutions ◽  
Constitutive Equations ◽  
Fractional Derivatives ◽  
Random Excitation ◽  
Bounded Noise ◽  
White Noise Process ◽  
Derivative Type ◽  
Axial Vibrations ◽  
Viscoelastic Rod

AbstractThe axial vibrations of a viscoelastic rod with a body attached to its end are investigated. The problem is modelled by the constitutive equations with fractional derivatives as well as with the perturbations involving a bounded noise and a white noise process. The weak solutions for the equations given below in two cases of constitutive equations as well as their stochastic moments are determined.

On a Noncompact Minimization Problem of Hardy-Sobolev Type

2002 ◽  
Vol 2 (1) ◽  
Author(s):  
K. Sandeep
Keyword(s):  
Minimization Problem ◽  
Sobolev Type ◽  
Existence And Nonexistence ◽  
Constraint Minimization

AbstractIn this paper we discuss the existence and nonexistence of minimizer for the constraint minimization problem

THE MOSER'S ITERATIVE METHOD FOR A CLASS OF ULTRAPARABOLIC EQUATIONS

2004 ◽  
Vol 06 (03) ◽  
pp. 395-417 ◽  
Author(s):  
ANDREA PASCUCCI ◽  
SERGIO POLIDORO
Keyword(s):  
Iterative Method ◽  
Weak Solutions ◽  
Ad Hoc ◽  
Iterative Scheme ◽  
Sobolev Type ◽  
Ultraparabolic Equation ◽  
Measurable Coefficients ◽  
Ultraparabolic Equations ◽  
Bounded Functions

We adapt the iterative scheme by Moser, to prove that the weak solutions to an ultraparabolic equation, with measurable coefficients, are locally bounded functions. Due to the strong degeneracy of the equation, our method differs from the classical one in that it is based on some ad hoc Sobolev type inequalities for solutions.

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