Construction of a Topological Degree Theory in Generalized Sobolev Spaces

Hammou, Mustapha Ait; Azroul, Elhoussine

doi:10.1007/978-3-030-02155-9_1

Cited by 4 publications

(2 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using another technical approach, that of the topological degree theory, and only with a growth condition, we prove in this paper the existence of at least one weak solution the problem (P). For more details about this theory and its applications, the reader can refer to [1,2,3,8] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

On a Nonlocal Problem Involving Fractional P(X, .)-Laplacian with Non-Standard Growth

Hammou¹

2022

AnnalsARSciMath

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

On a Nonlocal Problem Involving Fractional P(X, .)-Laplacian with Non-Standard Growth

Hammou¹

2022

AnnalsARSciMath

View full text Add to dashboard Cite

show abstract

“…The theory of topological degree has been widely used in the study of nonlinear dierential equations as a very eective tool, often those of elliptical type. For more details about the history of this theory and its use, the reader can refer, for example, to [1,2,3,4,5,8,9,11] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Existence of weak solutions for a nonlinear parabolic equations by Topological degree

Hammou

Azroul

2020

Advances in the Theory of Nonlinear Analysis and Its Application

Self Cite

View full text Add to dashboard Cite

We prove the existence of a weak solution for the nonlinear parabolic initial boundary value problem associated to the equation u t − div a(x, t, u, ∇u) = f (x, t), by using the Topological degree theory for operators of the form L + S, where L is a linear densely dened maximal monotone map and S is a bounded demicontinuous map of class (S + ) with respect to the domain of L. We will therefore use the Topological degree theory to study a parabolic equation in the space L p (0, T ; W 1,p 0 (Ω)) where the exponent p is not necessarily equal to 2 (p ≥ 2).

show abstract

Weak solutions for fractionalp(x,·)-Laplacian Dirichlet problems with weight

Hammou

2022

Analysis

View full text Add to dashboard Cite

The main purpose of this paper is to show the existence of weak solutions for a problem involving the fractional p ⁢ ( x , ⋅ ) {p(x,\cdot\,)} -Laplacian operator of the following form: { ( - Δ p ⁢ ( x , ⋅ ) ) s ⁢ u ⁢ ( x ) + w ⁢ ( x ) ⁢ | u | p ¯ ⁢ ( x ) - 2 ⁢ u = λ ⁢ f ⁢ ( x , u ) in ⁢ Ω , u = 0 in ⁢ ℝ N ∖ Ω , \left\{\begin{aligned} \displaystyle(-\Delta_{p(x,\cdot\,)})^{s}u(x)+w(x)% \lvert u\rvert^{\bar{p}(x)-2}u&\displaystyle=\lambda f(x,u)&&\displaystyle% \phantom{}\text{in }\Omega,\\ \displaystyle u&\displaystyle=0&&\displaystyle\phantom{}\text{in }\mathbb{R}^{% N}\setminus\Omega,\end{aligned}\right. The main tool used for this purpose is the Berkovits topological degree.

show abstract

Construction of a Topological Degree Theory in Generalized Sobolev Spaces

Cited by 4 publications

References 17 publications

On a Nonlocal Problem Involving Fractional P(X, .)-Laplacian with Non-Standard Growth

On a Nonlocal Problem Involving Fractional P(X, .)-Laplacian with Non-Standard Growth

Existence of weak solutions for a nonlinear parabolic equations by Topological degree

Weak solutions for fractionalp(x,·)-Laplacian Dirichlet problems with weight

Contact Info

Product

Resources

About