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| 開催情報 | 木曜日 16:00～17:30 数理科学研究科棟(駒場) 002号室 |
|---|---|
| 担当者 | 石毛 和弘 |
2008年07月10日(木)
16:00-17:30 数理科学研究科棟(駒場) 002号室
渡辺 達也 氏 (早稲田大学・理工学術院)
Two positive solutions for an inhomogeneous scalar field equation
渡辺 達也 氏 (早稲田大学・理工学術院)
Two positive solutions for an inhomogeneous scalar field equation
[ 講演概要 ]
We consider the following nonlinear elliptic equation:
−Deltau+u=g(u)+f(x),xinRN,
where Nge3. When f(x)equiv0, it is known that there is a nontrivial solution for a wide class of nonlinearities. Even though f(x)notequiv0, we can expect the existence of a nontrivial solution if f(x) is small in a suitable sense. Our purpose is to show the existence of two positive solutions via the variational approach when |f|L2 is small. The first solution is characterized as a local minimizer. The second solution will be obtained by the Mountain Pass Method. Since we do not impose any global condition on the nonlinearity, we will need a presice interaction estimate.
We consider the following nonlinear elliptic equation:
−Deltau+u=g(u)+f(x),xinRN,
where Nge3. When f(x)equiv0, it is known that there is a nontrivial solution for a wide class of nonlinearities. Even though f(x)notequiv0, we can expect the existence of a nontrivial solution if f(x) is small in a suitable sense. Our purpose is to show the existence of two positive solutions via the variational approach when |f|L2 is small. The first solution is characterized as a local minimizer. The second solution will be obtained by the Mountain Pass Method. Since we do not impose any global condition on the nonlinearity, we will need a presice interaction estimate.
