Differential equations with integral boundary conditions

Multiple positive solutions for first-order impulsive integral boundary value problems on time scales

“…In continuous case, since integral boundary value problems include two-point, three-point,..., npoint boundary value problems, such boundary value problems for continuous systems have received more and more attention and many results have worked out during the past ten years, see Refs. [21][22][23][24][25][26][27] for more details. To the best of authors' knowledge, up to the present, there is no paper concerning the boundary value problem with integral boundary conditions on time scales.…”

Generalized monotone iterative method for integral boundary value problems with causal operators

“…It is well known that monotone iterative technique is quite useful, see [3,13,14,15,16,17] and references therein. In [5,6,7,9,22], this method, combining upper and lower solutions, has been successfully applied to obtain the existence of extremal solutions for boundary value problems with integral boundary conditions. Bhaskar [4] and West [18] developed monotone iterative method, considered the generalized monotone iterative method for initial value problems, obtained the existence of extremal solutions for differential equations where the forcing function is the sum of two monotone functions, one of which is monotone non-decreasing and the other is non-increasing.…”

Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions

“…Monotone method for Riemann-Liouville fractional differential equations with initial conditions is developed by McRae [22] involving study of qualitative properties of solutions of initial value problem. Jankwoski [12] formulated some comparison results and obtained existence and uniqueness of solutions of differential equations with integral boundary conditions . Recently, Wang and Xie [29] developed monotone method and obtained existence and uniqueness of solution of fractional differential equation with integral boundary condition.…”