• Title/Summary/Keyword: Sturm-Liouville problem

Search Result 19, Processing Time 0.026 seconds

UNIQUENESS OF THE SOLUTION OF HALF INVERSE PROBLEM FOR THE IMPULSIVE STURM LIOUVILLE OPERATOR

  • Ozkan, A. Sinan;Keskin, Baki;Cakmak, Yasar
    • Bulletin of the Korean Mathematical Society
    • /
    • v.50 no.2
    • /
    • pp.499-506
    • /
    • 2013
  • The half-inverse spectral problem for an impulsive Sturm-Liouville operator consists in reconstruction of this operator from its spectrum and half of the potential. In this study, the spectrum of the impulsive Sturm-Liouville problem is given and by using the Hochstadt and Lieberman's method we show that if $q(x)$ is prescribed on (0, ${\frac{\pi}{2}}$), then only one spectrum is sufficient to determine $q(x)$ on the interval (0, ${\pi}$) for this problem.

THREE SOLUTIONS FOR A SECOND-ORDER STURM-LIOUVILLE EQUATION WITH IMPULSIVE EFFECTS

  • HAGHSHENAS, HADI;AFROUZI, GHASEM A.
    • Journal of applied mathematics & informatics
    • /
    • v.38 no.5_6
    • /
    • pp.407-414
    • /
    • 2020
  • In this article, a second-order Sturm-Liouville problem with impulsive effects and involving the one-dimensional p-Laplacian is considered. The existence of at least three weak solutions via variational methods and critical point theory is obtained.

POSITIVE SOLUTION FOR FOURTH-ORDER FOUR-POINT STURM-LIOUVILLE BOUNDARY VALUE PROBLEM

  • Sun, Jian-Ping;Wang, Xiao-Yun
    • Journal of applied mathematics & informatics
    • /
    • v.28 no.3_4
    • /
    • pp.679-686
    • /
    • 2010
  • This paper is concerned with the following fourth-order four-point Sturm-Liouville boundary value problem $u^{(4)}(t)=f(t,\;u(t),\;u^{\prime\prime}(t))$, $0\;{\leq}\;t\;{\leq}1$, ${\alpha}u(0)-{\beta}u^{\prime}(0)={\gamma}u(1)+{\delta}u^{\prime}(1)=0$, $au^{\prime\prime}(\xi_1)-bu^{\prime\prime\prime}(\xi_1)=cu^{\prime\prime}(\xi_2)+du^{\prime\prime\prime}(\xi_2)=0$. Some sufficient conditions are obtained for the existence of at least one positive solution to the above boundary value problem by using the well-known Guo-Krasnoselskii fixed point theorem.

ON THE INVERSE PROBLEM FOR STURM-LIOUVILLE OPERATOR WITH A NONLINEAR SPECTRAL PARAMETER IN THE BOUNDARY CONDITION

  • Mamedov, Khanlar R.
    • Journal of the Korean Mathematical Society
    • /
    • v.46 no.6
    • /
    • pp.1243-1254
    • /
    • 2009
  • The inverse scattering problem is investigated for some second order differential equation with a nonlinear spectral parameter in the boundary condition on the half line [0, $\infty$). In the present paper the coefficient of spectral parameter is not a pure imaginary number and the boundary value problem is not selfadjoint. We define the scattering data of the problem, derive the main integral equation and show that the potential is uniquely recovered.

DETERMINATION OF THE FLEXURAL RIGIDITY OF A BEAM FROM LIMITED BOUNDARY MEASUREMENTS

  • LESNIC DANIEL
    • Journal of applied mathematics & informatics
    • /
    • v.20 no.1_2
    • /
    • pp.17-34
    • /
    • 2006
  • Inverse coefficient identification problems associated with the fourth-order Sturm-Liouville operator in the steady state Euler-Bernoulli beam equation are investigated. Unlike previous studies in which spectral data are used as additional information, in this paper only boundary information is used, hence non-destructive tests can be employed in practical applications.

MULTIPLE SYMMETRIC POSITIVE SOLUTIONS OF A NEW KIND STURM-LIOUVILLE-LIKE BOUNDARY VALUE PROBLEM WITH ONE DIMENSIONAL p-LAPLACIAN

  • Zhao, Junfang;Ge, Weigao
    • Journal of applied mathematics & informatics
    • /
    • v.27 no.5_6
    • /
    • pp.1109-1118
    • /
    • 2009
  • In this paper, we are concerned with the following four point boundary value problem with one-dimensional p-Laplacian, $\{({\phi}_p(x'(t)))'+h(t)f(t,x(t),|x'(t)|)=0$, 0< t<1, $x'(0)-{\delta}x(\xi)=0,\;x'(1)+{\delta}x(\eta)=0$, where $\phi_p$ (s) = |s|$^{p-2}$, p > $\delta$ > 0, 1 > $\eta$ > $\xi$ > 0, ${\xi}+{\eta}$ = 1. By using a fixed point theorem in a cone, we obtain the existence of at least three symmetric positive solutions. The interesting point is that the boundary condition is a new Sturm-Liouville-like boundary condition, which has rarely been treated up to now.

  • PDF

PLANCHEREL AND PALEY-WIENER THEOREMS FOR AN INDEX INTEGRAL TRANSFORM

  • Kim, Vu--Tuan;Ali Ismail;Megumi Saigo
    • Journal of the Korean Mathematical Society
    • /
    • v.37 no.4
    • /
    • pp.545-563
    • /
    • 2000
  • An integral transform with the Bessel function Jv(z) in the kernel is considered. The transform is relatd to a singular Sturm-Liouville problem on a half line. This relation yields a Plancherel's theorem for the transform. A Paley-Wiener-type theorem for the transform is also derived.

  • PDF

EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS FOR SECOND-ORDER STURM-LIOUVILLE AND MULTI-POINT PROBLEMS ON TIME SCALES

  • Sang, Yan-Bin;Wei, Zhongli;Dong, Wei
    • Bulletin of the Korean Mathematical Society
    • /
    • v.48 no.5
    • /
    • pp.1047-1061
    • /
    • 2011
  • In this paper, a class of second-order boundary value problems with Sturm-Liouville boundary conditions or multi-point conditions is considered. Some existence and uniqueness theorems of positive solutions of the problem are obtained by using monotone iterative technique, the iterative sequences yielding approximate solutions are also given. The results are illustrated with an example.