Geodesic
Asymptotic behavior of solutions for some nonlinear partial differential equations on unbounded domains
Electronic journal of differential equations, Tome 2001 (2001)
We study the asymptotic behavior of positive solutions

$ -\Delta_p u({\bf x}) = V({\bf x}) u({\bf x})^{p-1}, \quad p greater than 1;\ {\bf x} \in \Omega,$

and related partial differential inequalities, as well as conditions for existence of such solutions. Here, $\Omega$ contains the exterior of a ball in $\mathbb{R}^N1 less than p less than N, \Delta_p$ is the p-Laplacian, and $V$ is a nonnegative function. Our methods include generalized Riccati transformations, comparison theorems, and the uncertainty principle.
Classification : 35B40, 35J60, 35J70
Keywords: p-Laplacian, Riccati, uncertainty principle 
@article{EJDE_2001__2001__a185,
     author = {Fleckinger,  Jacqueline and Harrell,  Evans M.II and de Th\'elin,  Fran\c{c}ois},
     title = {Asymptotic behavior of solutions for some nonlinear partial differential equations on unbounded domains},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0987.35062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a185/}
}
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AU  - de Thélin,  François
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JO  - Electronic journal of differential equations
PY  - 2001
VL  - 2001
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LA  - en
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%A de Thélin,  François
%T Asymptotic behavior of solutions for some nonlinear partial differential equations on unbounded domains
%J Electronic journal of differential equations
%D 2001
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%F EJDE_2001__2001__a185
Fleckinger,  Jacqueline; Harrell,  Evans M.II; de Thélin,  François. Asymptotic behavior of solutions for some nonlinear partial differential equations on unbounded domains. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a185/