Positive Solutions of Fractional Differential Equations with p-Laplacian

Abstract

The multiplicity of positive solution for a new class of four-point boundary value problem of fractional differential equations with -Laplacian operator is investigated. By the use of the Leggett-Williams fixed-point theorem, the multiplicity results of positive solution are obtained. An example is given to illustrate the main results.

Positive Solutions for a Hadamard Fractional p-Laplacian Three-Point Boundary Value Problem

“…where D α 0+ denotes the Riemann-Liouville fractional derivative. Positive solutions [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and nontrivial solutions [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] were also studied for fractional-order equations. For example, the authors in [16] used the Guo-Krasnoselskii's fixed-point theorem and the Leggett-Williams fixed-point theorem to study the existence and multiplicity of positive solutions for the fractional boundary-value problem…”

On positive solutions for some second-order three-point boundary value problems with convection term

“…In recent years, there has been much attention focused on questions of solutions of twopoint, three-point, multi-point, and integral boundary value problems for nonlinear ordinary differential equations and fractional differential equations. For example, two-point boundary value problems [3,15,29,39], beam equation problems [5,13,16,36], boundary value problems at resonance [2,6,42,43], fractional boundary value problems [8,24], impulsive problems [4,38], multi-point boundary value problems [10,14,20,25,26,32,33,43], integral boundary value problems [7,9,17,21,22,28,37], p-Laplace problems [11,13,24,27,30,31], delay problems [23,34,35], solitons [12], singular problems [3], Schrödinger problem [40,41], etc.…”

Monotone iterative method for a p-Laplacian boundary value problem with fractional conformable derivatives

“…Fractional p-Laplacian boundary value problems also received considerable attention, for example, see [16][17][18][19][20][21][22][23][24][25][26]. The literature on fractional differential equations equipped with integral boundary conditions also contains a variety of interesting results [27][28][29][30][31][32].…”