Monotone iterative method for semilinear impulsive evolution equations of mixed type in Banach spaces

Electronic Journal of Differential Equations

关键词: Initial value problem;    lower and upper solution;    impulsive integro-differential evolution equation;    C0-semigroup;    cone;   

DOI  :  

来源: DOAJ

【 摘 要 】

We use a monotone iterative method in the presence of lowerand upper solutions to discuss the existence and uniquenessof mild solutions for the initial value problem$$displaylines{u'(t)+Au(t)= f(t,u(t),Tu(t)),quad tin J,; t eq t_k,crDelta u |_{t=t_k}=I_k(u(t_k)) ,quad k=1,2,dots ,m,cru(0)=x_0,}$$where $A:D(A)subset Eo E$ is a closed linear operatorand $-A$ generates a strongly continuous semigroup$T(t)(tgeq 0)$ in $E$.Under wide monotonicity conditions and the non-compactness measurecondition of the nonlinearity f, we obtain theexistence of extremal mild solutions and a unique mild solutionbetween lower and upper solutions requiring only that $-A$generate a strongly continuous semigroup.

【 授权许可】

Unknown