October 3, 2025Open Access

On nonlinear elliptic problems with Hardy-Littlewood-Sobolev critical exponent and Sobolev-Hardy critical exponent

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Existence of solutions is established for nonlinear elliptic problems involving critical growth.
The study highlights the role of variational methods in addressing combined convolution-type and Hardy nonlinearity.
The application of critical exponent theories, including Hardy-Littlewood-Sobolev, is essential in this analysis.
This research may enable advancements in understanding complex mathematical behaviors in elliptic equations.

Implication

Variational methods establish solutions for nonlinear elliptic problems, suggesting significant mathematical implications.

Abstract

In this paper we use variational methods to establish the existence of solutions for a class of nonlinear elliptic problems involving a combined convolution-type and Hardy nonlinearity with subcritical and critical growth.

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Cite This Study

Gu et al. (2025) studied this question.

synapsesocial.com/papers/68e040e5a99c246f578b2e90 https://doi.org/10.48550/arxiv.2509.15806

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Implication

Variational methods establish solutions for nonlinear elliptic problems, suggesting significant mathematical implications.

On nonlinear elliptic problems with Hardy-Littlewood-Sobolev critical exponent and Sobolev-Hardy critical exponent

Key Points

Implication

Abstract

Discussion

Cite This Study

On nonlinear elliptic problems with Hardy-Littlewood-Sobolev critical exponent and Sobolev-Hardy critical exponent

Key Points

Implication

Abstract

Discussion

Cite This Study

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