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.