Anti-periodic boundary value problem for nonlinear first order ordinary differential equations

Some new results for BVPs of first-order nonlinear integro-differential equations of volterra type

“…Suppose there exist constants R >0, α ≥ 0 such that 22) where M(R) is a positive constant depending on R, B R = {x ℝ n , ||x|| ≤ R}. Then PBVP (1.1) has at least one solution x C with ||x|| C < R. Proof.…”

“…Furthermore, if A = B = I, where I denotes n × n identity matrix, then Ax(0)+Bx(1) = θ reduces to the so-called "anti-periodic" conditions x(0) = -x(1). The authors of [20][21][22][23][24] consider this kind of "anti-periodic" conditions for differential equations or impulsive differential equations. To the best of our knowledge it is the first article to deal with integro-differential equations with "anti-periodic" conditions so far.…”

Existence of Solutions to Anti-periodic Boundary Value Problem for Nonlinear Fractional Differential Equations

“…The existence of solutions to anti-periodic boundary value problems for firstorder ordinary differential equations was studied in [6,8,16,17]. In [15], Wang and Shen have studied the existence of solutions to anti-periodic boundary value problem for a second-order ordinary differential equation by using Schauder's fixed point theorem and the lower and upper solutions method.…”

The Anti-periodic Solutions Set for a Class of Nonlinear Evolution Inclusions in RN

“…The anti-periodic problems of evolution inclusions were investigated by Okochi [3], Aizicovici-McKibben-Reich [4], Franco-Nieto-O'Regan [5], Chen-Cho-O'Regan [6], Park-Ha [7], and Liu [8] and the references therein. In the past the topological structure of the solution set of differential inclusions in  R has been investigated by Himmelberg-Van Vleck [9] and DeBlasi-Myjak [10].…”