Nontrivial solutions for higher-order m-point boundary value problem with a sign-changing nonlinear term

Nontrivial Solutions for a Higher Order Nonlinear Fractional Boundary Value Problem Involving Riemann-Liouville Fractional Derivatives

“…Motivated by the aforementioned papers and some integer order equations [36][37][38][39], in this paper we use topological degree to study the existence of nontrivial solutions for the higher order nonlinear fractional boundary value problem (1). Our nonlinearity can be sign-changing and can also depend on the derivatives of unknown functions.…”

Existence of positive solutions of discrete third-order three-point BVP with sign-changing Green’s function

“…In 1992, Gupta [2] studied solvability of differential equation three-point boundary value problem. Soon afterwards, there arose many results on multi-point nonlinear boundary value problems [3][4][5][6]. In 1999, Ma [7] studied the existence of positive solution for a second-order differential equation three-point boundary value problem.…”

“…Without loss of generality, let η = 4. Then, by the direct calculation, we get θ ∈[5,6] Z . Choose θ = 5, then θ * = η+2-θ η+2 θ (Tθ )[2α(θ -1)] 2 -2α(T -1) a(s)…”

Positive solutions to one-dimensional quasilinear impulsive indefinite boundary value problems

“…On the other hand, we observe that many authors (see [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]) have paid more attention to a class of boundary value problems involving integral boundary conditions, which contains two-point, three-point, and general multi-point boundary value problems as exceptional cases, see [50][51][52][53][54][55][56][57][58] and the references cited therein.…”