• Title/Summary/Keyword: Differential Value

Search Result 1,102, Processing Time 0.027 seconds

EXISTENCE OF THREE POSITIVE SOLUTIONS OF A CLASS OF BVPS FOR SINGULAR SECOND ORDER DIFFERENTIAL SYSTEMS ON THE WHOLE LINE

  • Liu, Yuji;Yang, Pinghua
    • Journal of the Korean Mathematical Society
    • /
    • v.54 no.2
    • /
    • pp.359-380
    • /
    • 2017
  • This paper is concerned with a kind of boundary value problem for singular second order differential systems with Laplacian operators. Using a multiple fixed point theorem, sufficient conditions to guarantee the existence of at least three positive solutions of this kind of boundary value problem are established. An example is presented to illustrate the main results.

EXISTENCE OF THREE SOLUTIONS OF NON-HOMOGENEOUS BVPS FOR SINGULAR DIFFERENTIAL SYSTEMS WITH LAPLACIAN OPERATORS

  • Yang, Xiaohui;Liu, Yuji
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.29 no.2
    • /
    • pp.187-220
    • /
    • 2016
  • This paper is concerned with a kind of non-homogeneous boundary value problems for singular second order differential systems with Laplacian operators. Using multiple fixed point theorems, sufficient conditions to guarantee the existence of at least three solutions of this kind of boundary value problems are established. An example is presented to illustrate the main results.

Multiple Unbounded Positive Solutions for the Boundary Value Problems of the Singular Fractional Differential Equations

  • Liu, Yuji;Shi, Haiping;Liu, Xingyuan
    • Kyungpook Mathematical Journal
    • /
    • v.53 no.2
    • /
    • pp.257-271
    • /
    • 2013
  • In this article, we establish the existence of at least three unbounded positive solutions to a boundary-value problem of the nonlinear singular fractional differential equation. Our analysis relies on the well known fixed point theorems in the cones.

THE GROWTH OF SOLUTIONS OF COMPLEX DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENT HAVING FINITE DEFICIENT VALUE

  • Zhang, Guowei
    • Bulletin of the Korean Mathematical Society
    • /
    • v.58 no.6
    • /
    • pp.1495-1506
    • /
    • 2021
  • The growth of solutions of second order complex differential equations f" + A(z)f' + B(z)f = 0 with transcendental entire coefficients is considered. Assuming that A(z) has a finite deficient value and that B(z) has either Fabry gaps or a multiply connected Fatou component, it follows that all solutions are of infinite order of growth.

ON MEROMORPHIC SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL-DIFFERENCE EQUATIONS OF FIRST ORDER IN SEVERAL COMPLEX VARIABLES

  • Qibin Cheng;Yezhou Li;Zhixue Liu
    • Bulletin of the Korean Mathematical Society
    • /
    • v.60 no.2
    • /
    • pp.425-441
    • /
    • 2023
  • This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

OSCILLATIONS OF CERTAIN NONLINEAR DELAY PARABOLIC BOUNDARY VALUE PROBLEMS

  • Zhang, Liqin;Fu, Xilin
    • Journal of applied mathematics & informatics
    • /
    • v.8 no.1
    • /
    • pp.137-149
    • /
    • 2001
  • In this paper we consider some nonlinear parabolic partial differential equations with distributed deviating arguments and establish sufficient conditions for the oscillation of some boundary value problems.

Weighted Value Sharing and Uniqueness of Entire Functions

  • Sahoo, Pulak
    • Kyungpook Mathematical Journal
    • /
    • v.51 no.2
    • /
    • pp.145-164
    • /
    • 2011
  • In the paper, we study with weighted sharing method the uniqueness of entire functions concerning nonlinear differential polynomials sharing one value and prove two uniqueness theorems, first one of which generalizes some recent results in [10] and [16]. Our second theorem will supplement a result in [17].

SOLVING SECOND ORDER SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH LAYER BEHAVIOR VIA INITIAL VALUE METHOD

  • GEBEYAW, WONDWOSEN;ANDARGIE, AWOKE;ADAMU, GETACHEW
    • Journal of applied mathematics & informatics
    • /
    • v.36 no.3_4
    • /
    • pp.331-348
    • /
    • 2018
  • In this paper, an initial value method for solving a class of singularly perturbed delay differential equations with layer behavior is proposed. In this approach, first the given problem is modified in to an equivalent singularly perturbed problem by approximating the term containing the delay using Taylor series expansion. Then from the modified problem, two explicit Initial Value Problems which are independent of the perturbation parameter, ${\varepsilon}$, are produced: the reduced problem and boundary layer correction problem. Finally, these problems are solved analytically and combined to give an approximate asymptotic solution to the original problem. To demonstrate the efficiency and applicability of the proposed method three linear and one nonlinear test problems are considered. The effect of the delay on the layer behavior of the solution is also examined. It is observed that for very small ${\varepsilon}$ the present method approximates the exact solution very well.

A NEW FIFTH-ORDER WEIGHTED RUNGE-KUTTA ALGORITHM BASED ON HERONIAN MEAN FOR INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

  • CHANDRU, M.;PONALAGUSAMY, R.;ALPHONSE, P.J.A.
    • Journal of applied mathematics & informatics
    • /
    • v.35 no.1_2
    • /
    • pp.191-204
    • /
    • 2017
  • A new fifth-order weighted Runge-Kutta algorithm based on heronian mean for solving initial value problem in ordinary differential equations is considered in this paper. Comparisons in terms of numerical accuracy and size of the stability region between new proposed Runge-Kutta(5,5) algorithm, Runge-Kutta (5,5) based on Harmonic Mean, Runge-Kutta(5,5) based on Contra Harmonic Mean and Runge-Kutta(5,5) based on Geometric Mean are carried out as well. The problems, methods and comparison criteria are specified very carefully. Numerical experiments show that the new algorithm performs better than other three methods in solving variety of initial value problems. The error analysis is discussed and stability polynomials and regions have also been presented.