Sentence examples for method of sub from inspiring English sources

whose method of sub- and supersolution has been developed in [7, Chapter 5].

The aim of this paper is to establish the method of sub- and supersolutions for problem (1.1).

The method of sub- and supersolution for this kind of problems is a special case of [5].

Applying the method of sub- and supersolution (see [28]) corresponding to the order interval provides the existence of a smallest positive solution of problem (1.1) fulfilling.

By using the method of sub- and supersolutions and based on the results of S. Carl, we extend the theory for discontinuous problems.

Existence results for variational-hemivariational inequalities with or without the method of sub- and supersolutions have been obtained under different structure and regularity conditions on the nonlinear functions by various authors.

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

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

In particular, in [20], Han and Li obtained multiple positive, negative, and sign-changing solutions by combining the critical point theory and the method of sub-sup solutions for the (BVP) (1.2).

As g λ is sublinear, say, g λ = λ u q, 0 < q < 1, the monotone iteration scheme or the method of sub-solutions and super-solutions are effective; see [9].

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.