Sentence examples for maximal positive solution from inspiring English sources

Step 2. BVP (1.4) has a positive solution in, which is maximal positive solution.

Then, BVP (1.4) has minimal positive solution in and maximal positive solution in ; Moreover,, as uniformly on, where (2.22).

Step 3: BVP (1.1) has a positive solution in B r, which is a maximal positive solution.

Now, we apply Lemma 7.2 to the operator equation A x B x = x to yield that FHDE (2.1) has a minimal and a maximal positive solution in [ a, b ] defined on J.

Now, we apply Lemma 7.2 to the operator equation (AxBx = x ) to yield that BVPHDEF (1) has a minimal and a maximal positive solution in ([a, b]) defined on J.

Theorem 3.2 If f ∈ C ( [ 0, 1 ] × [ 0, + ∞ ), [ 0, + ∞ ) ), f ( t, u ) is nondecreasing in u and λ ∈ ( 0, + ∞ ), then BVP (1.1) has a minimal positive solution v ¯ in B r and a maximal positive solution w ¯ in B r.

Hence, by Theorem 2.5, BVP (3.1) has minimal and maximal positive solutions in.

Moreover, we develop two computable explicit monotone iterative sequences for approximating the two minimal and maximal positive solutions.

In [9 11], the authors obtained the minimal and maximal positive solutions by using a fixed point theorem of increasing operators.

We discuss the existence of minimal and maximal positive solutions for fractional differential equations with multipoint boundary value conditions, and new results are given.

In this paper, we consider the existence of minimal and maximal positive solutions for the following multiple-point boundary value problem: (1.4).