Existence of blow-up solutions for a class of elliptic systems

Alves, Claudianor O.; Holanda, Angelo R. F. de

doi:10.57262/die/1355867508

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2023

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Cited by 5 publications

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“…This is done in a smooth bounded domain Ω of R N , N ≥ 2, u, v > 0 in Ω, u| ∂Ω = +∞ and v| ∂Ω = +∞, where 1 < p, q < ∞ and ∆ t w = div(|∇w| t−2 ∇w) for any 1 < t < ∞. In an another work, Alves and de Holanda [1] studied the system ∆u = F u (x, u, v), ∆v = F v (x, u, v) from a variational point of view. However this approach does not apply to (1.2).…”

Section: Introductionmentioning

confidence: 99%

Existence of positive global radial solutions to nonlinear elliptic systems

Padhi

Dix

2023

ejde

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In this article we obtain global positive and radially symmetric solutions to the system of nonlinear elliptic equations $$ \operatorname{div}\big(\phi_j(|\nabla u|) \nabla u\big) +a_j(x)\phi_j(|\nabla u|) |\nabla u| =p_j(x)f_j(u_1(x),\dots,u_k(x))\,, $$ and in particular to Laplace's equation $$ \Delta u_j(x) =p_j(x)f_j(u_1(x),\dots,u_k(x))\,, $$ where $j=1,\dots,k$, $ x\in\mathbb{R}^N$, $N\geq 3$, $\Delta $ is the Laplacian operator, and $\nabla$ is the gradient. Also we state conditions for solutions to be bounded, and to be unbounded. With an example we illustrate our results. See also https://ejde.math.txstate.edu/special/02/p1/abstr.html

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Section: Introductionmentioning

confidence: 99%