Positivity of Two-Dimensional Elliptic Differential Operators with Nonlocal Conditions
Positivity of Two-Dimensional Elliptic Differential Operators with Nonlocal Conditions
In the present paper, the differential operator A defined by Au = −utt(t,x)−uxx(t,x)+ u(t,x) with domain D(A) = {u(t,x):utt,uxx,u∈C([0,1]×R),u(0,x) = u(1,x),ut(0,x) = ut(1,x),t∈[0, 1],x∈R} is considered. The Green function for A is constructed. The estimates for the Green function are obtained and the positivity of A in the Banach space …