Existence of a positive solution for problems with ( p , q ) $(p,q)$ -Laplacian and convection term in R N $\mathbb{R}^{N}$

Luiz FO Faria, Olimpio H Miyagaki, Mieko Tanaka
2016 Boundary Value Problems  
This paper provides a positive solution for the (p, q)-Laplace equation in R N with a nonlinear term depending on the gradient. The solution is constructed as the limit of positive solutions in bounded domains. Strengthening the growth condition, it is shown that the solution is also bounded. The positivity of the solution is obtained through a new comparison principle. Finally, under a stronger growth condition, we show the existence of a vanishing at infinity solution. MSC: 35J92; 35B51;
more » ... 35J92; 35B51; 35B50; 35B09; 35A16
doi:10.1186/s13661-016-0665-9 fatcat:cjtu7epbl5gptnlnjqi6rkdvs4