- Nonlinear semigroups on locally convex spaces
- Nonlinear semigroups on locally convex spaces
- ㆍ 저자명
- Hyeon. Son-Kuk
- ㆍ 간행물명
- The Pusan Kyongnam mathematical journal
- ㆍ 권/호정보
- 1990년|6권 1호|pp.111-121 (11 pages)
- ㆍ 발행정보
- 영남수학회
- ㆍ 파일정보
- 정기간행물|ENG| PDF텍스트
- ㆍ 주제분야
- 기타
Let E be a locally convex Hausdorff space and let $Gamma$ be a calibration for E. In this note we proved that if E is sequentially complete and a multi-vaiued operaturA in E is $Gamma$-accretive such that $D(A){subset}Re$ (I+$lambda$A) for all sufficiently small positive $lambda$, then A generates a nonlinear $Gamma$-contraction semiproup {T(t) ; t>0}. We also proved that if E is complete, $Gamma$ is a dually uniformly convex calibration, and an operator A is m-$Gamma$-accretive, then the initial value problem $${{frac{d}{dt}u(t)+Au(t); i;0,;t >0,atop u(0)=x}.$$ has a solution $u:[0,infty){ ightarrow}E$ given by $u(t)=T(t)x={lim}limit_{n ightarrowinfty}(I+frac{t}{n}A)^{-n}x$ each $x{varepsilon}D(A)$.