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

Abstract

In this paper, we consider a class of fractional differential equations with infinite-point boundary value conditions. Under some conditions concerning the spectral radius with respect to the relevant linear operator, both the existence of uniqueness and the nonexistence of positive solution are obtained by means of the iterative technique.

Nontrivial solutions for boundary value problems of a fourth order difference equation with sign-changing nonlinearity

“…where D p is the Riemann-Liouville fractional derivative, and f is a Lipschitz continuous function, with the Lipschitz constant associated with the first eigenvalue for the relevant operator. Using similar methods, the authors in [12,39,41] obtained some existence and nonexistence theorems for their problems. Motivated by the works mentioned above, we consider the existence of nontrivial solutions for (1.1) involving sign-changing nonlinearities.…”

Existence and Nonexistence of Positive Solutions for High-Order Fractional Differential Equation Boundary Value Problems at Resonance

“…Fractional-order models can describe many processes more accurately than integer-order models, and a great deal of papers focusing on FBVPs appeared in recent years (see [14][15][16][17][18][19][20][21][22][23]). e nonlocal FBVPs have especially drawn much attention (see [24][25][26][27][28][29][30][31]). For instance, in [14], the authors investigated the Dirichlet-type FBVP:…”

Existence and multiplicity of positive solutions for a class of singular fractional nonlocal boundary value problems

“…Recently, many results were obtained dealing with the fractional differential equations boundary value problems (FBVP) by the use of techniques of nonlinear analysis; see and the references therein. The nonlocal boundary value problems of fractional differential equation have particularly attracted a great deal of attention (see [25][26][27][28][29][30][31][32][33]). For example, a number of papers have been devoted to considering (1.1) under boundary value conditions (BC) as follows: In [12], Henderson and Luca considered the existence of positive solutions for a fractional differential equation subject to BC (1.3), where p ∈ [1, n -2], q ∈ [0, p].…”

“…For example, a number of papers have been devoted to considering (1.1) under boundary value conditions (BC) as follows: In [12], Henderson and Luca considered the existence of positive solutions for a fractional differential equation subject to BC (1.3), where p ∈ [1, n -2], q ∈ [0, p]. In [28], Wang and Liu considered a fractional differential equation with infinite-point boundary value conditions (1.4). In [29], by means of the fixed point index theory in cones, Wang et al established the existence and multiplicity results of positive solutions to (1.1) with BC (1.5).…”