Geodesic
Asymptotic behavior of solutions for some nonlinear partial differential equations on unbounded domains
Electronic journal of differential equations, Tome 2001 (2001)
Zbl   EuDML
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 
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__a107/
@article{EJDE_2001__2001__a107,
     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__a107/}
}
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