On a critical Schrödinger equation involving singular and vanishing potentials in RN

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This work aims to explore the existence and nonexistence of solutions to a specific class of Schrödinger equations with critical growth.
Analyzed critical Schrödinger equations of the form -Δu + |x|^a u = |x|^b |u|^{2^*(b) - 2}u + λ|x|^c |u|^{p-2}u in R^N
Established conditions for parameters a, b, c, and p ensuring valid solutions
Utilized mathematical frameworks to derive existence results under varying potential conditions.
Identified particular ranges for parameters where solutions exist or fail to exist
Demonstrated the influence of singular and vanishing potentials on solution behavior
Quantified critical growth effects on solution stability in R^N.

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Investigates critical growth solutions in higher-dimensional space, suggesting potential pathways for understanding complex equations.

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Carvalho et al. (2026) studied this question.

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