Double positive solutions for a nonlinear four-point boundary value problem with a -Laplacian operator

Multiple positive solutions for a class of nonlinear four-point boundary value problem with p-Laplacian

“…Motivated by the papers mentioned above, we shall consider in this paper the existence of multiple (at least three) positive solutions for nonlinear singular boundary value problem (1.1)-(1.2) by using Leggett-Williams fixed point theorem and Schauder fixed point theorem. The results obtained in this paper essentially improves and generalizes those results in the above mentioned references [6][7][8][9][10][11][12].…”

“…Recently, (1.1) together with some multi-point boundary value conditions have been studied by several researchers, for example, see [6][7][8][9][10][11][12].…”

“…More recently, in [11][12], the existence of a positive solution and double positive solutions of (1.1)-(1.2) has been discussed. The main tools are the fixed point index theory and the Avery-Henderson fixed point theorem on cone, respectively.…”

Positive Solutions for a Mixed-Order Three-Point Boundary Value Problem forp-Laplacian

“…The equation with a -Laplacian operator arises in the modeling of different physical and natural phenomena, non-Newtonian mechanics, nonlinear elasticity and glaciology, combustion theory, population biology, nonlinear flow laws, and so on. Liang et al in [1] used the fixed point theorem of Avery and Henderson to show the existence of at least two positive solutions. Zhao et al [2] studied the existence of at least three positive solutions by using Leggett-Williams fixed point theorem.…”

“…Motivated by the above works, we obtain some sufficient conditions for the existence of at least one and three positive solutions for (1) and (2).…”