Banach空间微分方程广义弱解的局部存在性

LOCAL EXISTENCE OF GENERALIZED WEAK SOLUTIONS FOR DIFFERENTIAL EQUATIONS IN A BANACH SPACE

在弱完备的实Banach空间E中考虑微分方程的Cauchy问题 :x′(t) =f(t,x(t) ) , x( 0 ) =x0 . (cp)其中x0 ∈E ,f:I×D→E(D E ,I R1 .通过使用弱非紧型条件给出 (cp)的广义弱解的局部存在性 ,完善 [1]、[2

In this paper,we consider the Cauchy problem for differential equations in a weakly complete Banach space E: x ′(t)=f(t,x(t)), x(0)=x 0.(cp) where x 0∈E,f:I×D→E(I=,DE).By using weak noncompact type's conditions,we obtain an existence theorem of generalized weak solutions to (cp),improving the results of weak solutions in ,.