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This paper studies a coupled system of nonlinear fractional differential equation with three-point boundary conditions. Applying the Schauder fixed point theorem, an existence result is proved for the following system D α u (t) = f (t, v (t) , D m v (t)) , t ∈ (0, 1) , D β v (t) = g (t, u (t) , D n u (t)) , t ∈ (0, 1) , u (0) = 0, D θ u (1) = δD θ u (η) , v(More)
We discuss the existence of positive solutions of a nonlinear nth order boundary value problem u (n) + a(t) f (u) = 0, t ∈ (0, 1) u(0) = 0, u (n−2) (0) = 0, αu(η) = u(1), where 0 < η < 1, 0 < αη n−1 < 1. In particular, we establish the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in(More)
We apply the generalized quasilinearization technique to obtain a monotone sequence of iterates converging quadratically to the unique solution of a general second order nonlinear differential equation with nonlinear nonlocal mixed three-point boundary conditions. The convergence of order n (n ≥ 2) of the sequence of iterates has also been established.
In the original Virtual Element space with degree of accuracy k, projector operators in the H 1-seminorm onto polynomials of degree ≤ k can be easily computed. On the other hand, projections in the L 2 norm are available only on polynomials of degree ≤ k − 2 (directly from the degrees of freedom). Here we present a variant of VEM that allows the exact(More)
In this paper, we study the existence of solutions for a boundary value problem of differential inclusions of order q ∈ (1, 2] with non-separated boundary conditions involving convex and non-convex multivalued maps. Our results are based on the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.
This paper studies a boundary value problem of nonlinear second-order q-difference equations with non-separated boundary conditions. As a first step, the given boundary value problem is converted to an equivalent integral operator equation by using the q-difference calculus. Then the existence and uniqueness of solutions of the problem is proved via the(More)