What question did this study set out to answer?

This research aims to investigate the existence of positive solutions for the fractional Laplace equation with singular and power-type nonlinear terms.

July 26, 2026Complex Variables and Elliptic Equations

Positive solutions of the fractional Laplace equation with singular nonlinear terms

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ZGZiyu GanHarbin Institute of Technology YZYongliang ZhouAnhui University

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Implication

Randomized trial examines positive solutions of the fractional Laplace equation with singular nonlinearities, suggesting key mathematical insights.

Key Points

This research aims to investigate the existence of positive solutions for the fractional Laplace equation with singular and power-type nonlinear terms.
Used variational methods on the Nehari manifold for 0<γ<1 to find distinct energy weak solutions.
Constructed a weak solution via sub- and supersolutions for general γ>0 and strong singular cases γ≥1.
Examined regularity of the weak solution after establishing existence.
Established existence of at least two distinct energy weak solutions for sufficiently small λ>0 when 0<γ<1.
Constructed weak solutions for general γ>0 and discussed properties of the solutions.
Provided insights into the regularity of the weak solutions.

Cite This Study

Gan et al. (2026) studied this question.

synapsesocial.com/papers/6a65a825d3aea3239cd78a00 https://doi.org/10.1080/17476933.2026.2704758

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Implication

Randomized trial examines positive solutions of the fractional Laplace equation with singular nonlinearities, suggesting key mathematical insights.

Positive solutions of the fractional Laplace equation with singular nonlinear terms

Discussion

Member takes

Implication

Key Points

Cite This Study

Positive solutions of the fractional Laplace equation with singular nonlinear terms

Discussion

Member takes

Implication

Key Points

Cite This Study

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