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Nonlinear elliptic model nonexistence assumption map

Family 370: The Lane–Emden and Hénon–Lane–Emden conjectures. First source-informed review, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Elliptic PDE researchers can screen a proposed entire positive solution against the weighted Hénon–Lane–Emden subcritical parameter inequality.

Applicability and commercial boundary

The nonexistence statement concerns entire-space solutions, origin continuity and classical behavior away from the origin. It does not forbid finite-domain solutions or make an engineering boundary-value solver unnecessary.

Initial business decision

Research infrastructure. Commercial demand and profitability remain hypotheses. Research usefulness is not evidence of a buyer budget.

Next verification action

Encode the exact dimension and exponent inequality with domain and regularity fields, then identify a research workflow that repeatedly uses it.

Evidence scope

The catalog statement and main-paper abstract or introductory theorem passages were individually reviewed. Available family-level scope documents were inspected, with attention to version differences and exclusions. This is a first application triage, not a full proof audit or independent Lean verification. Family 376 has nine paper abstracts inspected; selected scopes are not assumed to cover all nine papers in full. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.