Abstract
This paper deals with the existence and iteration of positive solutions for the following one-dimensional -Laplacian boundary value problems: , , subject to some boundary conditions. By making use of monotone iterative technique, not only we obtain the existence of positive solutions for the problems, but also we establish iterative schemes for approximating the solutions.
Highlights
We are concerned with the existence and iteration of positive solutions for the following one-dimensional p-Laplacian boundary value problems: φp utatft, u t, u t 0, t ∈ 0, 1, 1.1 subject to one of the following boundary conditions: u 0 0, αu 1 βu 1 0, 1.2 or γu 0 − δu 0 0, u 1 0, 1.3 where φp s following:
U, v is nondecreasing in u − v, t ∈ 0, 1, the proof is simple, here we omit it
U, v is nondecreasing in u − v, t ∈ 0, 1, and by assumptions H4 and H5, we obtain
Summary
We are concerned with the existence and iteration of positive solutions for the following one-dimensional p-Laplacian boundary value problems: φp utatft, u t , u t 0, t ∈ 0, 1 , 1.1 subject to one of the following boundary conditions:. In 6 , by using the monotone iterative technique, Ma et al obtained the existence of monotone positive solution and established the corresponding iterative schemes of 1.4 under the multipoint boundary value condition. In their discussion, the nonlinear term f is not involved with the first-order derivative u t. Motivated by the above-mentioned results, by making use of the classical monotone iterative technique, we will investigate the existence of positive solutions for the boundary value problems 1.1 , 1.2 and 1.1 , 1.3 , and give iterative schemes for approximating the solutions.
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