Twin positive solutions for singular nonlinear elliptic equations - Chen, Jianqing; Papageorgiou, Nikolaos S.; Rocha, Eugénio M. (Topological Methods in Nonlinear Analysis, 2010)
For a bounded domain ZR ^N with a C^2-boundary, we prove the existence of an ordered pair of smooth positive strong solutions for the nonlinear Dirichlet problem -Δ_p x(z) = β(z)x(z)^-η+f(z,x(z)) a.e on Z with xW^1,p_0(Z), which exhibits the combined effects of a singular term (η≥ 0) and a (p-1)-linear term f(z,x) near +∞, by using a combination of variational methods, with upper-lower solutions and with suitable truncation techniques.