Volume 15, Issue 4
Existence and Uniqueness of Radial Solutions of Quasilinear Equations in a Ball

Gongming Wei & Zuchi Chen

J. Part. Diff. Eq., 15 (2002), pp. 39-48.

Published online: 2002-11

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  • Abstract

We consider the boundary value problem for the quasilinear equation div(A(|Du|)Du) + f(u) = 0, u > 0, x ∈ B_R(0), u|_{∂B_R(0)} = 0, where A and f are continuous functions in (0, ∞) and f is positive in (0, 1), f(1) = 0. We prove that (1) if f is strictly decreasing, the problem has a unique classical radial solution for any real number R > 0; (2) if f is not monotonous, the problem has at least one classical radial solution for some R > 0 large enough.

  • Keywords

Quasilinear equations shooting argument radial classical solution

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@Article{JPDE-15-39, author = {}, title = {Existence and Uniqueness of Radial Solutions of Quasilinear Equations in a Ball}, journal = {Journal of Partial Differential Equations}, year = {2002}, volume = {15}, number = {4}, pages = {39--48}, abstract = { We consider the boundary value problem for the quasilinear equation div(A(|Du|)Du) + f(u) = 0, u > 0, x ∈ B_R(0), u|_{∂B_R(0)} = 0, where A and f are continuous functions in (0, ∞) and f is positive in (0, 1), f(1) = 0. We prove that (1) if f is strictly decreasing, the problem has a unique classical radial solution for any real number R > 0; (2) if f is not monotonous, the problem has at least one classical radial solution for some R > 0 large enough.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5460.html} }
TY - JOUR T1 - Existence and Uniqueness of Radial Solutions of Quasilinear Equations in a Ball JO - Journal of Partial Differential Equations VL - 4 SP - 39 EP - 48 PY - 2002 DA - 2002/11 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5460.html KW - Quasilinear equations KW - shooting argument KW - radial classical solution AB - We consider the boundary value problem for the quasilinear equation div(A(|Du|)Du) + f(u) = 0, u > 0, x ∈ B_R(0), u|_{∂B_R(0)} = 0, where A and f are continuous functions in (0, ∞) and f is positive in (0, 1), f(1) = 0. We prove that (1) if f is strictly decreasing, the problem has a unique classical radial solution for any real number R > 0; (2) if f is not monotonous, the problem has at least one classical radial solution for some R > 0 large enough.
Gongming Wei & Zuchi Chen . (2019). Existence and Uniqueness of Radial Solutions of Quasilinear Equations in a Ball. Journal of Partial Differential Equations. 15 (4). 39-48. doi:
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