Geodesic
Positive Solutions of Quasilinear Elliptic Equations
Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 202-211

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This paper is concerned with existence theorems for positive solutions of the Dirichlet problem for quasilinear elliptic differential equation containing a gradient term. Using the shooting method and the a priori estimates for the first zero, we obtain sufficient conditions for the existence of classical positive solutions of the problem in the ball. 
@article{MZM_2005_78_2_a4,
     author = {E. I. Galakhov},
     title = {Positive {Solutions} of {Quasilinear} {Elliptic} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {202--211},
     publisher = {mathdoc},
     volume = {78},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_2_a4/}
}
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E. I. Galakhov. Positive Solutions of Quasilinear Elliptic Equations. Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 202-211. http://geodesic.mathdoc.fr/item/MZM_2005_78_2_a4/