A Note on Entire Large Solutions to Semilinear Elliptic Systems of Competitive Type

Authors

Alan V. Lair, Air Force Institute of TechnologyFollow

Document Type

Article

Publication Date

7-15-2025

Abstract

We consider the elliptic system Δu = p(|x|)u^av^b, Δv = q(|x|)u^cv^d on Rⁿ (n ≥ 3) where a, b, c, d are positive constants with min {a,d} >1, and the functions p and q are positive and continuous. We establish conditions on p and q, along with the exponents a, b, c, d, which ensure the existence of a positive entire solution satisfying lim_|x|→∞ u(x) = lim_|x|→∞ v(x) = ∞.

Comments

This article is accepted for inclusion in the December 2025 issue of Nonlinear Analysis.

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DOI

10.1016/j.na.2025.113903

Source Publication

Nonlinear Analysis (ISSN 0362-546X | eISSN 1873-5215)

Recommended Citation

Lair, A. V. (2025). A Note on entire large solutions to semilinear elliptic systems of competitive type. Nonlinear Analysis, 261, 113903. https://doi.org/10.1016/j.na.2025.113903