Asymptotic behavior up to the second order term of solutions to quasilinear elliptic singular problems

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• 作者：Ester Giarrusso^a ; ^{ester.giarrusso@unina.it" class="auth_mail" title="E-mail the corresponding author} ; Giovanni Porru^b ; ^{porru@unica.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35J25 ; 35J61 ; 35B40
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：145
• 期：Complete
• 页码：49-67
• 全文大小：645 K

文摘

Let Ω⊂R^N$\Omega \subset {\mathbb{R}}^N$ be a bounded smooth domain. We prove the existence of a positive solution to the problem Δu=−u^−γ|∇u|^q$\Delta u=-u^{-\gamma }{\left|\nabla u\right|}^q$ in Ω$\Omega$, u=0$u=0$ on ∂Ω$\partial \Omega$, with 35" title="Click to view the MathML source">γ>1$\gamma >1$ and 35c81dc8ff72b73783e5ade4c7d6" title="Click to view the MathML source">0<q<1$0<q<1$. Furthermore, for γ>3$\gamma >3$ and 0<q≤(γ−3)/(γ−2)$0<q\le (\gamma -3)/(\gamma -2)$ we find asymptotic expansions up to the second order of a solution u$u$ in terms of the distance from x$x$ to the boundary ∂Ω$\partial \Omega$.