Sentence examples for super solutions from inspiring English sources

They're keen to emphasize their merits—stating they work with some of the most powerful tools on the planet, create new software, hardware, and super solutions that no one has ever heard of.

A vector function defined on, for some, is called a sub (or super) solution of ( 1.1 )–( 1.3 ), if all the following hold: (1) ; (2) for, and for almost all ; (3) (2.1)  .

Our results are obtained via the method of sub-super solutions.

We discuss the existence of positive solution via sub-super solutions without assuming sign conditions on f(0), h(0).

They got the existence and multiplicity of positive solutions result for some combined sublinear condition by the method of sub-super solutions.

f, h, a, b are C1 non-decreasing functions satisfying a(0) ≥ 0, b(0) ≥ 0. Using the method of sub-super solutions, we prove the existence of weak solution.

Our approach makes use of the theory of regular variation and a new perturbation method for constructing sub- and super-solutions.

We show that in general the comparison principle between the sub- and super-solutions does not hold, and there is no uniqueness of either a viscosity solution or a minimizer of this free boundary problem by constructing counter-examples in various cases in any dimension.

The experimental results show that the proposed method can not only generate images in higher quality, but also satisfy the requirement of real-time video super-solution.

By means of the theory of linear equations and constructing self-similar super-solutions and sub-solutions, we obtain a critical global existence curve.

They first established a sub-supersolution theorem and then proved, under some structural conditions, that the problem had at least one weak solution in (W^{1,p}_{0}(Omega)) by constructing ordered sub- and super-solutions.