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This is a Quantitative Study study.

September 29, 2025Open Access

Multiplicity results for mixed local-nonlocal equations with singular and critical exponential nonlinearity in R²

Key Points

The study identifies at least two positive weak solutions for mixed local-nonlocal singular problems in R^2.
Key evidence from the findings reveals that the presence of critical exponential nonlinearity is crucial to the results.
The approach utilizes a combination of sub-solution super-solution techniques and variational methods to draw conclusions.
This research highlights a novel inclusion of a variable singular exponent in the context of these equations.

Abstract

In this article, we prove the existence of at least two positive weak solutions for a mixed local-nonlocal singular problem in the presence of critical exponential nonlinearity in dimension two. The novelty of this work is the inclusion of a variable singular exponent in the context of mixed operator and critical exponential nonlinearity in R². Our approach is based on sub-solution super-solution technique, combined with variational methods.

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Cite This Study

S. Biswas (Tue,) studied this question.

synapsesocial.com/papers/68da58c9c1728099cfd10976 https://doi.org/https://doi.org/10.48550/arxiv.2503.08261

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