[PDF] Top 20 Nonlinear second-order impulsive q-difference Langevin equation with boundary conditions

... Nowadays there is a significant increase of activities in the area of q-calculus due to its applications in various fields such as mathematics, mechanics, and physics. The book by Kac and Cheung [] covers many of ... See full document

... Note that the operator A : U → PC(J, R) is continuous and completely continuous. From the choice of U, there is no x ∈ ∂U such that x = θ Ax for some θ ∈ (, ). Consequently, by the nonlinear alternative of ... See full document

... A quantum calculus substitute the classical derivative by a difference operator, which al- lows one to deal with sets of non-differentiable functions. There are many different types of quantum difference operators such as ... See full document

... has been studied by many authors; see [–] and the references therein. Here y(k) = y(k +)–y(k) for all k ∈ Z, p, q : I → R are functions, f : I × R → R is a continuous function. In , Agarwal and O’Regan [] ... See full document

... The q-difference equations initiated at the beginning of the twentieth century [–] is a very interesting field in difference ...of boundary value problems (BVPs) for nonlinear q-difference ... See full document

... Note that the linear part of the periodic BVP (1.2) is not necessarily invertible, that is, we may be unable to equivalently rewrite (1.2) in the integral form. However, if we use Lemma 2.1, then impulsive BVP ... See full document

... introduce conditions to be used in the next ...singular nonlinear integro-differential equations are presented to demonstrate the application of the main ... See full document

... Nonlocal boundary-value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects, ...three-point nonlinear boundary ... See full document

... Fractional calculus is a generalization of integer order calculus [, ]. It has been used by many researchers to adequately describe the evolution of a variety of engineering, eco- nomical, physical, and ... See full document

... nonlocal boundary value problem of nonlinear implicit impulsive Langevin equation involving mixed order ...Sufficient conditions are constructed to discuss the qualitative ... See full document

... In the present paper we prove existence and uniqueness results for the impulsive bound- ary value problem (.) by using Banach’s contraction mapping principle and Krasnosel- skii’s fixed-point theorem. The rest of ... See full document

... Theorem 2.2 (Nonlinear alternative for single valued maps)[24]. Let E be a Banach space, C a closed, convex subset of E, U an open subset of C and 0 Î U. Suppose that F: Ū ® C is a continuous, compact (that is, F( ... See full document

... In this paper, we study a nonlocal boundary value problem for a second-order Hahn difference equation. Our problem contains two Hahn difference operators with different numbers of q and ω ... See full document

... ficient conditions on the existence of nontrivial homoclinic solutions that have both of the components not identically zero to system ...the boundary value problems are for difference equations, and less is ... See full document

... We discuss the existence of optimal controls for a Lagrange problem of systems governed by the second-order nonlinear impulsive di ff erential equations in infinite dimensional spaces. We apply ... See full document

... from conditions (15) that only the even coe ffi cients of the corresponding recursion operators provide us with canonical conservation laws of equation (5), whereas in the case of first order ... See full document

... In Section 2, instead of Schauder estimates, we will derive higher order derivative estimates for solutions of 1.1, 1.2 when the boundary conditions are degenerate elliptic but strictly [r] ... See full document

... The quantum calculus (calculus without limits or q-calculus) is concerned with differ- ence operators and allows one to deal with sets of nondifferentiable functions. Quantum difference operators appear in several ... See full document

... In this paper, the existence and uniqueness of solutions for an impulsive mixed boundary value problem of nonlinear differential equations of fractional order are obtained. Our results are ... See full document

... for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point ... See full document