2017年1月
Generalized Joseph-Lundgren exponent and intersection properties for supercritical quasilinear elliptic equations
ARCHIV DER MATHEMATIK
- ,
- 巻
- 108
- 号
- 1
- 開始ページ
- 71
- 終了ページ
- 83
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1007/s00013-016-0969-0
- 出版者・発行元
- 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 < r < infinity,
u(0) = rho > 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 >= 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.
{r(-(gamma-1))(r(alpha)vertical bar u'vertical bar(beta-1u') + vertical bar u vertical bar(p-1) u = 0, 0 < r < infinity,
u(0) = rho > 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 >= 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 : 7
Web of Science ® の 関連論文(Related Records®)ビュー
- リンク情報
- ID情報
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- DOI : 10.1007/s00013-016-0969-0
- ISSN : 0003-889X
- eISSN : 1420-8938
- Web of Science ID : WOS:000392503200008