## Taiwanese Journal of Mathematics

### EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SINGULAR SOLUTIONS OF QUASILINEAR ELLIPTIC EQUATIONS IN Rn

Jann-Long Chern

#### Abstract

In this paper we consider the quasilinear elliptic equation \def\theequation{1} $${\rm div}(|\nabla u|^{m-2}\nabla u)+f(u)=0$$ where $n\gt m\gt 1$. We obtain a necessary and sufficient condition for the existence of positive radial solutions $u=u(r)$ on $[r_0, \infty)$, where $r_0 \gt 0$. If $f$ satisfies a further condition, then Eq. (1) possesses infinitely many singular ground state solutions $u(r)$ satisfying $u(r)\sim r^{-{(n-m)}\over {m-1}}$ at $\infty$ and $u(r)\to \infty \hbox{\ as\ }r\to 0^+$. We also obtain some important conclusions via our main results.

#### Article information

Source
Taiwanese J. Math., Volume 1, Number 2 (1997), 195-207.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405237

Digital Object Identifier
doi:10.11650/twjm/1500405237

Mathematical Reviews number (MathSciNet)
MR1452096

Zentralblatt MATH identifier
0877.35041

#### Citation

Chern, Jann-Long. EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SINGULAR SOLUTIONS OF QUASILINEAR ELLIPTIC EQUATIONS IN Rn. Taiwanese J. Math. 1 (1997), no. 2, 195--207. doi:10.11650/twjm/1500405237. https://projecteuclid.org/euclid.twjm/1500405237