Combined effects in nonlinear problems arising in the study of   anisotropic continuous media
  The paper deals with the study of a Lane-Emden-Fowler equation with Dirichlet boundary condition and variable potential functions. The analysis developed in this paper combines monotonicity methods with variational arguments. Remark (April 21, 2020): Our results were later studied also by D.-P. Covei, Quasilinear problems with the competition between convex and concave nonlinearities and variable potentials, Internat. J. Math. 24:1 (2013), art. 1350005), arXiv:1104.4626v1. 
Vicen\c{t}iu D. R\u{a}dulescu and Du\v{s}an D. Repov\v{s}
math.AP