Asymptotic Behavior of Solutions for Some Nonlinear Partial Differential Equations on Unbounded Domains
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We study the asymptotic behavior of positive solutions u of
-∆pu(x) = V(x)u(x)p-1, p > 1; x ∈ Ω,
and related partial differential inequalities, as well as conditions for existence of such solutions. Here, Ω contains the exterior of a ball in ℝN 1 < p < N, ∆p is the p-Laplacian and V is a nonnegative function. Our methods include generalized Riccati transformations, comparison theorems, and the uncertainty principle.
CitationFleckinger, J., Harrell, E. M., & de Thelin, F. (2001). Asymptotic behavior of solutions for some nonlinear partial differential equations on unbounded domains. Electronic Journal of Differential Equations, 2001(77), pp. 1-14.
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