Existence Results for Neumann Problem with Critical Sobolev–Hardy Exponent and Choquard-Type Nonlinearity

Zhenfeng Zhang; Calogero Vetro; Tianqing An; Wei Chen

doi:10.3390/fractalfract9090574

August 30, 2025Fractal and FractionalOpen Access

Existence Results for Neumann Problem with Critical Sobolev–Hardy Exponent and Choquard-Type Nonlinearity

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Key Points

Existence of solutions for Neumann problems is established.
Key techniques involve the Nehari manifold method addressing both subcritical and critical cases.
The study focuses on fractional Laplacians coupled with Choquard-type nonlinearities.
Findings indicate critical Sobolev–Hardy exponent behavior in various scenarios.

Implication

Analysis reveals existence of solutions for Neumann problems involving fractional Laplacians, highlighting critical Sobolev–Hardy behavior.

Abstract

We consider a Neumann problem for the fractional Laplacian involving a nonlocal Choquard-type nonlinearity and Sobolev–Hardy exponent. Under suitable assumptions on the data and using the Nehari manifold method, we discuss the existence problem in several subcritical and critical cases.

Discussion

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Cite This Study

Zhang et al. (2025) studied this question.

synapsesocial.com/papers/68c182529b7b07f3a060ed5f https://doi.org/10.3390/fractalfract9090574

View Full Paper

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Existence Results for Neumann Problem with Critical Sobolev–Hardy Exponent and Choquard-Type Nonlinearity

Key Points

Implication

Abstract

Discussion

Cite This Study

Existence Results for Neumann Problem with Critical Sobolev–Hardy Exponent and Choquard-Type Nonlinearity

Key Points

Implication

Abstract

Discussion

Cite This Study

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