2017年1月

# Generalized Joseph-Lundgren exponent and intersection properties for supercritical quasilinear elliptic equations

ARCHIV DER MATHEMATIK
• Yasuhito Miyamoto
• ,
• Kazune Takahashi

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DOI
10.1007/s00013-016-0969-0

SPRINGER BASEL AG

We study the solution u(r, rho) of the quasilinear elliptic problem
{r(-(gamma-1))(r(alpha)vertical bar u'vertical bar(beta-1u') + vertical bar u vertical bar(p-1) u = 0, 0 &lt; r &lt; infinity,
u(0) = rho &gt; 0, u' =0.
The usual Laplace, m-Laplace, and k-Hessian operators are included in the differential operator r(-(gamma-1))(r(alpha)vertical bar u'vertical bar(beta-1)u'. Under certain conditions on alpha, beta, gamma, and p, the equation has a singular positive solution u*(r) and the solution u(r, rho) is positive for r &gt;= 0. We study the intersection numbers between u(r, rho) and u*(r) and between u(r,rho(0)) and u(r,rho(1)). A generalized Joseph-Lundgren exponent p*JL plays a crucial role. The main technique is a phase plane analysis. In particular, we use two changes of variables which transform the equation into two autonomous systems.

Web of Science ® 被引用回数 : 6

リンク情報
DOI
https://doi.org/10.1007/s00013-016-0969-0
Web of Science