Explosive Solutions of Elliptic Equations with Absorption and Non-Linear Gradient Term

Proceedings Mathematical Sciences

VicenÅ£iu Rădulescu¹  Marius Ghergu²  Constantin Niculescu¹ 

[1] $$;Department of Mathematics, University of Craiova, 00 Craiova, Romania$$

关键词: Explosive solution;    semilinear elliptic problem;    entire solution;    maximum principle.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let 𝑓 be a non-decreasing $C^1$-function such that $f > 0$ on $(0, ∞), f(0) = 0, int_1^∞ 1/sqrt{F(t)}dt < ∞$ and $F(t)/f^{2/a}(t)→ 0$ as $t →∞$, where $F(t) = int_0^t f(s)ds$ and $a in (0,2]$. We prove the existence of positive large solutions to the equation $𝛥 u + q(x)|abla u|^a = p(x) f(u)$ in a smooth bounded domain $𝛺subset R^N$, provided that 𝑝, 𝑞 are non-negative continuous functions so that any zero of 𝑝 is surrounded by a surface strictly included in 𝛺 on which 𝑝 is positive. Under additional hypotheses on 𝑝 we deduce the existence of solutions if 𝛺 is unbounded.

【 授权许可】

Unknown