• Title, Summary, Keyword: boundary value problem

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MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEM WITH FINITE FRACTIONAL DIFFERENCE

  • He, Yansheng;Hou, Chengmin
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.2
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    • pp.173-186
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    • 2015
  • In this paper, we consider a discrete fractional nonlinear boundary value problem in which nonlinear term f is involved with the fractional order difference. We transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.

ANALYSIS OF SOME NONLOCAL BOUNDARY VALUE PROBLEMS ASSOCIATED WITH FEEDBACK CONTROL

  • Lee, Hyung-Chun
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.2
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    • pp.325-338
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    • 1998
  • Some nonlocal boundary value problems which arise from a feedback control problem are considered. We give a precise statement of the mathematical problems and then prove the existence and uniqueness of the solutions. We consider the Dirichlet type boundary value problem and the Neumann type boundary value problem with nonlinear boundary conditions. We also provide a regularity results for the solutions.

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UNIQUENESS OF SOLUTIONS FOR THE BOUNDARY VALUE PROBLEM OF CERTAIN NONLINEAR ELLIPTIC OPERATORS VIA p-HARMONIC BOUNDARY

  • Lee, Yong Hah
    • Communications of the Korean Mathematical Society
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    • v.32 no.4
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    • pp.1025-1031
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    • 2017
  • We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.

THE INITIAL-BOUNDARY-VALUE PROBLEM OF A GENERALIZED BOUSSINESQ EQUATION ON THE HALF LINE

  • Xue, Ruying
    • Journal of the Korean Mathematical Society
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    • v.45 no.1
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    • pp.79-95
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    • 2008
  • The local existence of solutions for the initial-boundary value problem of a generalized Boussinesq equation on the half line is considered. The approach consists of replacing he Fourier transform in the initial value problem by the Laplace transform and making use of modern methods for the study of nonlinear dispersive wave equation

THE METHOD OF QUASILINEARIZATION AND A THREE-POINT BOUNDARY VALUE PROBLEM

  • Eloe, Paul W.;Gao, Yang
    • Journal of the Korean Mathematical Society
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    • v.39 no.2
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    • pp.319-330
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    • 2002
  • The method of quasilinearization generates a monotone iteration scheme whose iterates converge quadratically to a unique solution of the problem at hand. In this paper, we apply the method to two families of three-point boundary value problems for second order ordinary differential equations: Linear boundary conditions and nonlinear boundary conditions are addressed independently. For linear boundary conditions, an appropriate Green\`s function is constructed. Fer nonlinear boundary conditions, we show that these nonlinearities can be addressed similarly to the nonlinearities in the differential equation.

POSITIVE SOLUTIONS TO A FOUR-POINT BOUNDARY VALUE PROBLEM OF HIGHER-ORDER DIFFERENTIAL EQUATION WITH A P-LAPLACIAN

  • Pang, Huihui;Lian, Hairong;Ge, Weigao
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.59-74
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    • 2010
  • In this paper, we obtain the existence of positive solutions for a quasi-linear four-point boundary value problem of higher-order differential equation. By using the fixed point index theorem and imposing some conditions on f, the existence of positive solutions to a higher-order four-point boundary value problem with a p-Laplacian is obtained.