Existence result of second-order differential equations with integral boundary conditions at resonance

Abstract

By using Mawhin's continuation theorem, some sufficient conditions for the existence of solution for a class of second-order differential equations with integral boundary conditions at resonance are established, which are complement of previously known results. The interesting point is that we shall deal with the case dim Ker L = 2, which will cause some difficulties in constructing the projector Q . Since all the existence results obtained in previous papers are for the case dim Ker L = 1, our work is new.

The Existence of Positive Solution to a Nonlinear Fractional Differential Equation with Integral Boundary Conditions

“…It is worth mentioning that there are still many problems that remain open in this vital field other than the results obtained in this paper: for example, whether or not we can study the fractional differential equations with integral boundary conditions at resonance see, e.g., 27 , and whether or not we can give a unified approach applicable to many BVPs see, e.g., 28-31 . More efforts are still needed in the future.…”

Existence results for fractional order differential equation with nonlocal Erdélyi–Kober and generalized Riemann–Liouville type integral boundary conditions at resonance

“…Integral boundary value problems have also gained many people's attention and have been applied to many fields, such as physics, chemistry, and engineering, see [11,13,22,[29][30][31]35]. Besides, the subject of fractional differential equations has attracted much attention, see [1-5, 7, 10, 12, 15, 23, 24, 27, 28, 32-34, 36-39, 42].…”

Resonant p-Laplacian problems with functional boundary conditions

“…Mawhin's continuation theorem [1] and its extension by Ge and Ren [2] are effective tools in the study of boundary value problems at resonance (see [3][4][5][6][7][8][9][10] and the references therein). In Refs.…”