Geodesic
On monotonicity of solutions of Dirichlet problem for some quasilinear elliptic equations in half-spaces
Eurasian mathematical journal, Tome 6 (2015) no. 4, pp. 59-76

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We prove the monotonicity of nonnegative bounded solutions to the Dirichlet problem for a quasilinear elliptic equation of the form $-\Delta_p u=f(u)g(x_n)$ with $p\geqslant3$ in a half-space, where $x_n$ is the normal coordinate of the argument. This assertion implies new nonexistence results for the case $f(u)=u^q$ with the appropriate values of $q$. 
@article{EMJ_2015_6_4_a5,
     author = {O. A. Salieva},
     title = {On monotonicity of solutions of {Dirichlet} problem for some quasilinear elliptic equations in half-spaces},
     journal = {Eurasian mathematical journal},
     pages = {59--76},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2015_6_4_a5/}
}
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O. A. Salieva. On monotonicity of solutions of Dirichlet problem for some quasilinear elliptic equations in half-spaces. Eurasian mathematical journal, Tome 6 (2015) no. 4, pp. 59-76. http://geodesic.mathdoc.fr/item/EMJ_2015_6_4_a5/