An Existence Result for a Class of p(x)—Anisotropic Type Equations

Ourraoui, Anass; Ragusa, Maria Alessandra

doi:10.3390/sym13040633

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2024

Publication Types

Select...

Article5

Relationship

Self Cite1

Independent4

Authors

Journals

Cited by 8 publications

(1 citation statement)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, anisotropic type problems in the subcritical case have received specific attention in recent decades. We refer the reader to the papers Boureanu et al [23,43], Fan [44], Ji [45], Mihǎilescu et al [46,47], Ourraoui and Ragusa [48], and Rǎdulescu and Repovš [49], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Existence and multiplicity of solutions for a class of critical anisotropic elliptic equations of Schrödinger–Kirchhoff‐type

Eddine

Nguyen

Ragusa

2023

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Existence and multiplicity of solutions for a class of critical anisotropic elliptic equations of Schrödinger–Kirchhoff‐type

Eddine

Nguyen

Ragusa

2023

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

Equivalence and regularity of weak and viscosity solutions for the anisotropic $${{\textbf {p}}}(\cdot )$$-Laplacian

Ochoa,

Valverde

2024

Nonlinear Differ. Equ. Appl.

View full text Add to dashboard Cite

On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications

Chems Eddine,

Ragusa,

Repovš

2024

Fract Calc Appl Anal

View full text Add to dashboard Cite

We obtain critical embeddings and the concentration-compactness principle for the anisotropic variable exponent Sobolev spaces. As an application of these results,we confirm the existence of and find infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters. With the groundwork laid in this work, there is potential for future extensions, particularly in extending the concentration-compactness principle to anisotropic fractional order Sobolev spaces with variable exponents in bounded domains. This extension could find applications in solving the generalized fractional Brezis–Nirenberg problem.

show abstract

An Existence Result for a Class of p(x)—Anisotropic Type Equations

Abstract: In this paper, we study a class of anisotropic variable exponent problems involving the p→(.)-Laplacian. By using the variational method as our main tool, we present a result regarding the existence of solutions without the so-called Ambrosetti–Rabinowitz-type conditions.

Cited by 8 publications

References 21 publications

Existence and multiplicity of solutions for a class of critical anisotropic elliptic equations of Schrödinger–Kirchhoff‐type

Existence and multiplicity of solutions for a class of critical anisotropic elliptic equations of Schrödinger–Kirchhoff‐type

Equivalence and regularity of weak and viscosity solutions for the anisotropic $${{\textbf {p}}}(\cdot )$$-Laplacian

On the concentration-compactness principle for anisotropic variable exponent Sobolev spaces and its applications

Contact Info

Product

Resources

About