Asymptotic shape of a solution for the Plasma problem in higher dimensional spaces
Masataka Shibata
Communications on Pure & Applied Analysis 2003, 2(2): 259-275 doi: 10.3934/cpaa.2003.2.259
We consider asymptotic shape of a solution for a semilinear elliptic equation in dimensions 3 or over, by using singular perturbation technique. The equations arise in the Plasma Problem. The solution is obtained as a global minimizer of some energy functional. Precisely energy estimates and uniqueness of a solution for limiting problem gives information about asymptotic shape of a solution.
keywords: Singular perturbations.
Asymptotic behavior of positive solutions for a class of quasilinear elliptic equations with general nonlinearities
Shinji Adachi Masataka Shibata Tatsuya Watanabe
Communications on Pure & Applied Analysis 2014, 13(1): 97-118 doi: 10.3934/cpaa.2014.13.97
We study the asymptotic behavior of the ground state for a class of quasilinear Schrödinger equations with general nonlinearities. By the variational argument and dual approach, we show the asymptotic non-degeneracy and uniqueness of the ground state.
keywords: Quasilinear elliptic equation asymptotic behavior.

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