Sentence examples for be any nonnegative solution from inspiring English sources

Let (Phi_{t}(X_{0})=Phi t,X_{0}):=(S t), e(cdot,t), i(cdot,t), T t))) be any nonnegative solution of system (1.4) with the boundary conditions (1.5) and the initial condition (1.6).

Let be a nonnegative solution of (1.11).

Let u be a nonnegative solution of (1.1) and (1.2).

Under the assumption [IU] (i.e., the associated heat kernel is intrinsically ultracontractive), we establish an integral representation theorem: any nonnegative solution is represented uniquely by an integral on (D×{0})∪(∂MD×[0,T)), where ∂MD is the Martin boundary of D for the associated elliptic operator.

Moreover, is a nonnegative solution to (2.19).

Thus is a nonnegative solution of (1.1)−(1.4).

Assume that holds, and is a nonnegative solution of (1.11).

By Lemma 2.2, is a nonnegative solution of (1.5).

Hence ( λ, U ) is a nonnegative solution of (3.25).

Assume that and is a nonnegative solution of (1.11).

Thus, u is a nonnegative solution of (1 -(4).