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arXiv · 2407.14408

Two Infinite Families of Solutions for Singular Superlinear Equations on Exterior Domains

Ali Diwan·Joseph Iaia
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Abstract

In this paper, we study radial solutions of $\Delta u + K(|x|)f(u) = 0$ in the exterior of the ball of radius $R > 0$ in $\mathbb{R}^N$ with $ N > 2$ where $f$ grows superlinearly at infinity and is singular at 0 with $f \sim \frac{1}{|u|^{q-1}u}$ where $0 < q < 1.$ We also assume $ K(r) \sim |r|^{- \alpha}$ for large $r$ and establish the existence of two infinite families of solutions when $ N + q(N-2) < \alpha < 2(N-1).$

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Ali Diwan, Joseph Iaia. 2024-07-19. Two Infinite Families of Solutions for Singular Superlinear Equations on Exterior Domains. https://arxiv.org/abs/2407.14408

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