Positive solutions for a class of fractional 3-point boundary value problems at resonance

Abstract

In this paper, we study the nonlocal fractional differential equation:continuous. The existence and uniqueness of positive solutions are obtained by means of the fixed point index theory and iterative technique.

Positive solutions for a class of fractional infinite-point boundary value problems

“…), FDE serve as an excellent instrument for the description of memory and hereditary properties of various materials and processes. During the last few decades, much attention has been paid to the study of boundary value problems (BVP for short) of fractional differential equation, such as the nonlocal BVP [1,3,7,13,18], singular BVP [6,8,11,19,20,25], semipositone BVP [14][15][16]23], resonant BVP [2,12], and impulsive BVP [10,27]. Since only positive solutions are meaningful in most practical problems, some work has been done to study the existence of positive solutions for fractional boundary value problems by using the techniques of nonlinear analysis.…”

Positive Solutions to n-Order Fractional Differential Equation with Parameter

“…Fractional differential equations BVP has become a hot issue; see the monographs of Lakshmikantham and Vatsala [1], Rudin [2], Samko et al [3], Agarwal et al [4,5], and Webb and Zima [6]. Many excellent results have been reported; see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In [24], El-Sayed and Bin-Taher study the following m-point BVP:…”

A New Approach to the Existence of Quasiperiodic Solutions for Second-Order Asymmetric p-Laplacian Differential Equations

“…In recent years, all kinds of nonlinear dynamic behavior, such as the existence of positive solutions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and signchanging solutions [17,18], the existence and uniqueness of solutions [19][20][21][22][23][24][25], the existence and multiplicity results [26][27][28][29][30], and the existence of unbounded solutions [31,32], have been widely investigated for some nonlinear ordinary differential equations and partial differential equations due to the application in many fields such as physics, mechanics, and the engineering technique fields. In the present paper, we deal with the existence of Aubry-Mather sets and quasiperiodic solutions for the second-order differential equations with a -Laplacian and an asymmetric nonlinear term…”

“…In this paper, we will deal with this interesting problem and answer this question in the form of Theorem 1 with more general case (1) than that of (5). Because of the presence of weak smoothness nonlinearity, the methods of seeking the existence of Aubry-Mather sets and quasiperiodic solutions for problems as [38,39] do not seem to be applicable to (1). This phenomenon provokes some mathematical difficulties, which make the study of (1) particularly interesting.…”