On a New Class of Weak Solutions to the Spatially Homogeneous Boltzmann and Landau Equations

1998 ◽  
Vol 143 (3) ◽  
pp. 273-307 ◽  
Author(s):  
Cédric Villani
Keyword(s):  
Weak Solutions ◽  
New Class ◽  
Spatially Homogeneous

scholarly journals Existence of Weak Solutions for a New Class of Fractional p-Laplacian Boundary Value Systems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 475 ◽  
Author(s):  
Fares Kamache ◽  
Rafik Guefaifia ◽  
Salah Boulaaras ◽  
Asma Alharbi
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Value Systems ◽  
Existence Of Weak Solutions ◽  
New Class ◽  
Two Parameters

In this paper, at least three weak solutions were obtained for a new class of dual non-linear dual-Laplace systems according to two parameters by using variational methods combined with a critical point theory due to Bonano and Marano. Two examples are given to illustrate our main results applications.

scholarly journals EXISTENCE OF 3-WEAK SOLUTIONS FOR A NEW CLASS OF AN OVERDETERMINED SYSTEM OF FRACTIONAL PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040036 ◽  
Author(s):  
SALAH BOULAARAS ◽  
RAFIK GUEFAIFIA ◽  
ASMA ALHARBI ◽  
BAHRI CHERIF
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Critical Point ◽  
Differential System ◽  
Point Theorem ◽  
Weak Solutions ◽  
Overdetermined System ◽  
Critical Point Theorem ◽  
New Class

The paper deals with the existence of three different weak solutions of [Formula: see text] -Laplacian fractional for an overdetermined nonlinear fractional partial Fredholm–Volterra integro-differential system by using variational methods combined with a critical point theorem due to Bonanno and Marano.

scholarly journals Existence of Positive Weak Solutions for a New Class of p,q Laplacian Nonlinear Elliptic System with Sign-Changing Weights

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Rafik Guefaifia ◽  
Salah Mahmoud Boulaaras ◽  
Sultan Alodhaibi ◽  
Salem Alkhalaf
Keyword(s):  
Elliptic System ◽  
Positive Solutions ◽  
Weak Solutions ◽  
Nonlinear Elliptic System ◽  
Bounded Domains ◽  
New Class ◽  
Nonlinear Elliptic ◽  
Sign Conditions

In this paper, by using subsuper solutions method, we study the existence of weak positive solutions for a new class of p,q Laplacian nonlinear elliptic system in bounded domains, when ax, bx,αx, and βx are sign-changing functions that maybe negative near the boundary, without assuming sign conditions on f0,g0,h0, and γ0.

scholarly journals Existence and multiplicity of positive weak solutions for a new class of (P; Q)-Laplacian systems

2020 ◽  
Vol 21 (2) ◽  
pp. 861
Author(s):  
Rafik Guefaifia ◽  
Salah Boulaaras ◽  
Jiabin Zuo ◽  
Praveen Agarwal
Keyword(s):  
Weak Solutions ◽  
New Class ◽  
Existence And Multiplicity

scholarly journals A New Proof of the Existence of Nonzero Weak Solutions of Impulsive Fractional Boundary Value Problems

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 856
Author(s):  
Asma Alharbi ◽  
Rafik Guefaifia ◽  
Salah Boulaaras
Keyword(s):  
Boundary Value Problems ◽  
Weak Solutions ◽  
Boundary Value ◽  
Linking Theorem ◽  
New Class ◽  
Fractional Boundary Value Problems

The paper deals with the existence of at least two non zero weak solutions to a new class of impulsive fractional boundary value problems via Brezis and Nirenberg’s Linking Theorem. Finally, an example is presented to illustrate our results.

scholarly journals A new class of spatially homogeneous 4D string backgrounds

1995 ◽  
Vol 353 (4) ◽  
pp. 450-456 ◽  
Author(s):  
Nikolaos A Batakis
Keyword(s):  
New Class ◽  
Spatially Homogeneous

scholarly journals On Existence of Multiplicity of Weak Solutions for a New Class of Nonlinear Fractional Boundary Value Systems via Variational Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Fares Kamache ◽  
Salah Mahmoud Boulaaras ◽  
Rafik Guefaifia ◽  
Nguyen Thanh Chung ◽  
Bahri Belkacem Cherif ◽  
...  
Keyword(s):  
Variational Methods ◽  
Weak Solutions ◽  
Variational Approach ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Value Systems ◽  
Critical Point Theorem ◽  
New Class ◽  
Left And Right

This paper deals with the existence of solutions for a new class of nonlinear fractional boundary value systems involving the left and right Riemann-Liouville fractional derivatives. More precisely, we establish the existence of at least three weak solutions for the problem using variational methods combined with the critical point theorem due to Bonano and Marano. In addition, some examples in ℝ 3 and ℝ 4 are given to illustrate the theoritical results.

scholarly journals On Existence of Sequences of Weak Solutions of Fractional Systems with Lipschitz Nonlinearity

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Rafik Guefaifia ◽  
Salah Mahmoud Boulaaras ◽  
Adel Abd Elaziz El-Sayed ◽  
Mohamed Abdalla ◽  
Bahri-Belkacem Cherif
Keyword(s):  
Nonlinear System ◽  
Variational Method ◽  
Fractional Order ◽  
Weak Solutions ◽  
Infinitely Many Solutions ◽  
Control Parameters ◽  
Fractional Systems ◽  
New Class ◽  
Lipschitz Nonlinearity

In this article, the variational method together with two control parameters is used for introducing the proof for the existence of infinitely many solutions for a new class of perturbed nonlinear system having p -Laplacian fractional-order differentiation.

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