New Insights on Keller–Osserman Conditions for Semilinear Systems

Dragos-Patru Covei ()
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Dragos-Patru Covei: The Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana, 1st District, 010374 București, Romania

Mathematics, 2024, vol. 13, issue 1, 1-10

Abstract: In this article, we consider a semilinear elliptic system involving gradient terms of the form Δ y x + λ 1 ∇ y x = p x f y x , z x i f x ∈ Ω , Δ z x + λ 2 ∇ z x = q x g y x i f x ∈ Ω , where λ 1 , λ 2 ∈ 0 , ∞ , Ω is either a ball of radius R > 0 or the entire space R N . Based on certain standard assumptions regarding the potential functions p and q , we introduce new conditions on the nonlinearities f and g to investigate the existence of entire large solutions for the given system. The method employed is successive approximation. Additionally, for specific cases of p , q , f and g , we employ Python code to plot the graph of both the numerical solution and the exact solution.

Keywords: Keller–Osserman conditions; existence of solutions; entire solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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