Existence and iteration of positive solutions for a singular two-point boundary value problem with a p-Laplacian operator

Abstract

Abstract. In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation (ϕp(u )) + q(t)f (u) = 0, 0 < t < 1, where ϕp(s) := |s| p−2 s, p > 1, subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient q(t) may be singular at t = 0, 1.

Existence of solutions for a multi-point boundary value problem with a p ( r ) $p(r)$ -Laplacian

“…In this paper, we are concerned with a class of differential equations involving a p(r)-Laplacian operator. The addressed equation with the multi-point boundary value is quite different from the related references discussed in the literature [26][27][28]32]. The nonlinear differential system studied in the present paper is more generalized and more practical.…”

“…(1.1) subjected to some other boundary conditions becomes the classical p-Laplacian problem, which has been extensively researched in [19][20][21] and we have obtained the existence of solutions for the addressed equations. For more information on the problems of differential equations with p-Laplacian operator, the readers may refer to [22][23][24][25][26][27][28][29][30]. This paper focuses on the following p(r)-Laplacian differential equations with multipoint boundary conditions: where the functions f , p, a and the constants α, β i , ξ , η i (1 ≤ i ≤ m -3) satisfy:…”

“…, p(r) > 1, a ∈ C((0, 1), R) is possibly singular at r = 0 or r = 1 and satisfies 0 < 1 0 |a(r)| dr < +∞; (H2) α, β i > 0, 0 < ξ < η 1 < η 2 < • • • < η m-3 < 1. Compared with some new achievements in the articles, such as [19][20][21][22][23][24][25][26][27][28][29][30], the major contributions of our research contain at least the following three:…”

Existence and iteration of positive solutions to third order three-point BVP with increasing homeomorphism and positive homomorphism

“…We recall that we have already used the technique of iteration to study BVP with a p−Laplacian operator, for example [6,10]. The following similar problem to BVP (1) has been studied in [10], (17) (φ p (u )) (t) = q(t)f (t, u(t)), 0 ≤ t ≤ 1, But, in [10], when we rewrite the BVP (17) into an equivalent integral equation, an unknown parameter must be included in the integral equation.…”