Asymptotics for quasilinear elliptic non-positone problems

Zuodong Yang¹ ; Qishao Lu¹

¹ College of Science Beijing University of Aeronautics and Astronautics Beijing, China, 100083

Annales Polonici Mathematici, Tome 79 (2002) no. 1, pp. 85-95

Résumé

In the recent years, many results have been established on positive solutions for boundary value problems of the form $$\displaylines{ -\mathop{\rm div}\nolimits (|\nabla u(x)|^{p-2}\nabla u(x))=\lambda f(u(x))\ \quad \hbox{in }\ {\mit\Omega}, \cr u(x)=0\quad\ \hbox{on }\ \partial{\mit\Omega}, \cr}$$ where $ \lambda>0$, ${\mit\Omega} $ is a bounded smooth domain and $ f(s)\geq 0 $ for $ s\geq 0$. In this paper, a priori estimates of positive radial solutions are presented when $ N > p>1$, ${\mit\Omega} $ is an $N$-ball or an annulus and $ f\in C^1(0,\infty)\cup C^0([0,\infty))$ with $f(0)0$ (non-positone).

Détail

DOI : 10.4064/ap79-1-7

Keywords: recent years many results have established positive solutions boundary value problems form displaylines mathop div nolimits nabla p nabla lambda quad hbox mit omega quad hbox partial mit omega where lambda mit omega bounded smooth domain geq geq paper priori estimates positive radial solutions presented mit omega n ball annulus infty cup infty non positone