TY - JOUR
AU - Chen, Jianqing
AU - Papageorgiou, Nikolaos S.
AU - Rocha, EugĂ©nio M.
PY - 2010/04/23
Y2 - 2024/10/08
TI - Twin positive solutions for singular nonlinear elliptic equations
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 35
IS - 1
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2010.011
SP - 187 - 201
AB - For a bounded domain $Z\subseteq{\mathbb{R}}^N$ with a $C^2$-boundary, we prove the existenceof an ordered pair of smooth positive strong solutions for the nonlinear Dirichlet problem$$-\Delta_p x(z) = \beta(z)x(z)^{-\eta}+f(z,x(z))\quad \text{a.e on } Z\text{ with } x\in W^{1,p}_0(Z),$$which exhibits the combined effects of a singular term ($\eta\geq 0$) and a $(p-1)$-linear term $f(z,x)$ near $+\infty$, by using a combination of variational methods, with upper-lower solutions and with suitable truncation techniques.
ER -