Existence of multiple positive solutions for nth-order p-Laplacian m-point singular boundary value problems

Abstract

In this paper, by using fixed point theorem, we prove the existence of multiple positive solutions for a class of nth-order p-Laplacian m-point singular boundary value problem. The interesting point is that the nonlinear term f explicitly involves the each-order derivative of variable u(t).Keywords p-Laplacian operator · nth-order m-point singular boundary value problem · Positive solutions · Fixed points Mathematics Subject Classification (2000) 34B10 · 34B16 · 34B18

Existence of positive solutions fornth-orderp-Laplacian singular super-linear boundary value problems

“…Using the Krasnosel'skii, Leggett-Williams fixed-point theorems, the authors in papers [5][6][7][8][9][10][11] have given some sufficient conditions for the existence of positive solution and multiple positive solutions for a class of nth-order m-point singular boundary value problems. By constructing lower and upper solutions and with the comparison theorem, Z.L.…”

“…By constructing lower and upper solutions and with the comparison theorem, Z.L. Now, in this paper, we shall give some necessary and sufficient conditions for the existence of S n−2 p positive solutions as well as S n−1 p positive solutions of the singular super-linear boundary value problems (1.1) by using the fixed point theorems on cones, which are different from that of [5][6][7][8][9][10][11][12]. Now, in this paper, we shall give some necessary and sufficient conditions for the existence of S n−2 p positive solutions as well as S n−1 p positive solutions of the singular super-linear boundary value problems (1.1) by using the fixed point theorems on cones, which are different from that of [5][6][7][8][9][10][11][12].…”

Positive solutions of the system for nth-order singular nonlocal boundary value problems

“…The existence of positive solutions for nonlinear nth-order nonlocal boundary value problems has been studied by many authors, see [1][2][3][4][5][6][7][8] and references therein. However, to our knowledge, the existence of positive solutions for the system of nonlinear nth-order singular nonlocal boundary value problems has not been studied as yet.…”