On the radially symmetric solutions of a BVP for a class of nonlinear elliptic partial differential equations

J. Hegedûs, Bolyai Institute, Szeged, Hungary

E. J. Qualitative Theory of Diff. Equ., Proc. 6'th Coll. Qualitative Theory of Diff. Equ., No. 12. (2000), pp. 1-16.

Abstract: Uniqueness and comparison theorems are proved for the BVP of the form
$$\Delta u(x)+g(x,u(x),\ |\nabla u(x)|)=0,\quad x\in B, u|_\Gamma=a\in {\openo R}\ (\Gamma:=\partial B),$$
where $B$ is the unit ball in ${\openo R}^n$ centered at the origin $(n\ge2).$ We investigate radially symmetric solutions, their dependence on the parameter $a\in{\openo R}$, and their concavity.

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