October 16, 2025Open Access

Nonexistence of positive radial solutions for semipositone ϕ-Laplacian problems with superlinear reaction term

Puntos clave

No positive radial solutions exist for a class of semipositone ϕ-laplacian problems with superlinear reaction terms.
For sufficiently large λ, it is shown that positive solutions are impossible, relying on both indirect arguments and energy analysis.
The study reveals the significance of the function f, connecting its negative value at zero to its behavior as it approaches infinity.
Using the ϕ-laplacian operator, we explore the dynamics within the unit ball, contributing to theoretical aspects of this mathematical domain.

Resumen

The aim of this paper is to prove the nonexistence of positive radial solutions to the problem -Δ_ϕu=λf (u), x B₁ (0), u (x) =0 on |x|=1, for λ>0 sufficiently large. Here, ϕ is a continuous function, Δ_ϕ denotes the ϕ-Laplacian operator which is defined by Δ_ϕ (u): =div (ϕ (| u|) u), and B₁ (0) is the unit ball in RN, with N>1. Furthermore, f is a continuous, nondecreasing function such that f (0) <0, and its behavior at infinity is intimately related to ϕ. Our findings are presented in a combined format, employing both an indirect argument and an energy analysis.

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Cite This Study

Herrón et al. (Fri,) studied this question.

synapsesocial.com/papers/68f0f51d8dd8ea469b1d717f https://doi.org/https://doi.org/10.48550/arxiv.2508.05930

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