Regions of existence for a class of nonlinear diffusion type problems

Abstract

The regions of existence are established for a class of two point nonlinear diffusion type boundary value problems (NDBVP)where a1 > 0, a2 ≥ 0, C ∈ R. These problems arise very frequently in many branches of engineering, applied mathematics, astronomy, biological system and modern science (see [1,3,4,8,14,15]). By using the concept of upper and lower solutions with monotone constructive technique, we derive some sufficient conditions for existence in the regions where ∂f ∂s ≥ 0 and ∂f ∂s ≤ 0. Theoretical methods are applied for a set of problems which arise in real life.

Analysis difficulties students’ mathematics problem-solving in material SPLDV at junior high school

“…R3 made several errors: a) type A error, where the student was mistaken in reading the script question and understanding the main objective of the question; b) type B error: read the question thoroughly but fail to understand the contents; c) type C, where students cannot apply model mathematics to the question. Should subject R3 lists, especially formerly method next/previous use, to know the intended result (Kelly, 2020;Verma et al,, 2020). However, subject R3 only supplied A little answer; even then, results were picked from friends.…”

A Review on a Class of Second Order Nonlinear Singular BVPs

“…)y (x) = 0, (quasi derivative) by Verma et al[230], to −(p(x)y (x)) = q(x) f (x, y, py ), 0 < x < 1, y (0) = 0, y (1) = 0, (x = 0 is a regular singular point) in Verma[231].Verma et al[232] used a monotone iterative technique and computed regions of existence for a class of two point nonlinear diffusion type boundary value problems−s (x) − ns (x) − m x s (x) = f (x, s), m > 0, n ∈ R, x ∈ (0, 1), s(0)= 0, a 1 s(1) + a 2 s (1) = C,…”