Existence Results for Singular <i>p</i>-Biharmonic Problem with HARDY Potential and Critical Hardy-Sobolev Exponent

Existence Results for Singular <i>p</i>-Biharmonic Problem with HARDY Potential and Critical Hardy-Sobolev Exponent

In this article, we consider the singular <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi></mrow></semantics></math></inline-formula>-biharmonic problem involv...

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Bibliographic Details
Main Author: Gurpreet Singh
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Axioms
Subjects:
p-biharmonic problem
Choquard equation
ground state solution
least-energy sign-changing solution
Online Access:https://www.mdpi.com/2075-1680/14/4/304
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Summary:In this article, we consider the singular <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi></mrow></semantics></math></inline-formula>-biharmonic problem involving Hardy potential and critical Hardy–Sobolev exponent. Firstly, we study the existence of ground state solutions by using the minimization method on the associated Nehari manifold. Then, we investigate the least-energy sign-changing solutions by considering the Nehari nodal set. In both cases, the critical Sobolev exponent is of great importance as the solutions exists only if we are below the critical Sobolev exponent.
ISSN:2075-1680

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