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COAR Access Rights: open accessSubject: Green's function

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Now showing 1 - 3 of 3
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    Article
    Citation - WoS: 35
    Citation - Scopus: 43
    Lyapunov-Type Inequalities for Mixed Non-Linear Forced Differential Equations Within Conformable Derivatives
    (Springer, 2018) Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, Jehad; Jarad, Fahd; Ozbekler, Abdullah
    We state and prove new generalized Lyapunov-type and Hartman-type inequalities fora conformable boundary value problem of order alpha is an element of (1,2] with mixed non-linearities of the form ((T alpha X)-X-a)(t) + r(1)(t)vertical bar X(t)vertical bar(eta-1) X(t) + r(2)(t)vertical bar x(t)vertical bar(delta-1) X(t) = g(t), t is an element of (a, b), satisfying the Dirichlet boundary conditions x(a) = x(b) = 0, where r(1), r(2), and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0 < eta < 1 < delta < 2. Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative T-alpha(a) is replaced by a sequential conformable derivative T-alpha(a) circle T-alpha(a), alpha is an element of (1/2,1]. The potential functions r(1), r(2) as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.
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    Article
    Citation - WoS: 16
    Citation - Scopus: 19
    An Expansion Result for a Sturm-Liouville Eigenvalue Problem With Impulse
    (Tubitak Scientific & Technological Research Council Turkey, 2010) Faydaoglu, Serife; Guseinov, Gusein Sh
    The paper is concerned with an eigenvalue problem for second order differential equations with impulse. Such a problem arises when the method of separation of variables applies to the heat conduction equation for two-layered composite. The existence of a countably infinite set of eigenvalues and eigenfunctions is proved and a uniformly convergent expansion formula in the eigenfunctions is established.
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    Article
    On the Resolvent of the Laplace-Beltrami Operator in Hyperbolic Space
    (Cambridge Univ Press, 2015) Guseinov, Gusein Sh.
    In this paper, a detailed description of the resolvent of the Laplace-Beltrami operator in n-dimensional hyperbolic space is given. The resolvent is an integral operator with the kernel (Green's function) being a solution of a hypergeometric differential equation. Asymptotic analysis of the solution of this equation is carried out.