• 제목/요약/키워드: Positive solutions

검색결과 744건 처리시간 0.026초

THE NEHARI MANIFOLD APPROACH FOR DIRICHLET PROBLEM INVOLVING THE p(x)-LAPLACIAN EQUATION

  • Mashiyev, Rabil A.;Ogras, Sezai;Yucedag, Zehra;Avci, Mustafa
    • 대한수학회지
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    • 제47권4호
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    • pp.845-860
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    • 2010
  • In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.

EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR THE SYSTEMS OF HIGHER ORDER BOUNDARY VALUE PROBLEMS ON TIME SCALES

  • Rao, A. Kameswara
    • Journal of applied mathematics & informatics
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    • 제33권1_2호
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    • pp.1-12
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    • 2015
  • This paper is concerned with boundary value problems for systems of n-th order dynamic equations on time scales. Under the suitable conditions, the existence and multiplicity of positive solutions are established by using abstract fixed-point theorems.

MULTIPLE POSITIVE SOLUTIONS OF INTEGRAL BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

  • Liu, Xiping;Jin, Jingfu;Jia, Mei
    • Journal of applied mathematics & informatics
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    • 제30권1_2호
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    • pp.305-320
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    • 2012
  • In this paper, we study a class of integral boundary value problems for fractional differential equations. By using some fixed point theorems, the results of existence of at least three positive solutions for the boundary value problems are obtained.

BIFURCATION ANALYSIS OF A SINGLE SPECIES REACTION-DIFFUSION MODEL WITH NONLOCAL DELAY

  • Zhou, Jun
    • 대한수학회지
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    • 제57권1호
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    • pp.249-281
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    • 2020
  • A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.

MULTIPLE POSITIVE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEMS WITH IMPULSE

  • Song, Xiaohua;Zhao, Zengqin;Wang, Xin
    • Journal of applied mathematics & informatics
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    • 제27권3_4호
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    • pp.875-883
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    • 2009
  • At least two positive solutions of a first-order periodic boundary value problem with impulse are obtained by establishing a new cone and the theorem of fixed point index. And at the end of this paper we give an example to illustrate the application of our main results.

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POSITIVE SOLUTIONS OF THE SECOND-ORDER SYSTEM OF DIFFERENTIAL EQUATIONS IN BANACH SPACES

  • Cao, Jianxin;Chen, Haibo;Deng, Jin
    • Journal of applied mathematics & informatics
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    • 제28권5_6호
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    • pp.1445-1460
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    • 2010
  • In this paper, a second-order system of multi-point boundary value problems in Banach spaces is investigated. Based on a specially constructed cone and the fixed point theorem of strict-set-contraction operators, the criterion of the existence and multiplicity of positive solutions are established. And two examples demonstrating the theoretic results are given.

Positive Solutions for Three-point Boundary Value Problem of Nonlinear Fractional q-difference Equation

  • Yang, Wengui
    • Kyungpook Mathematical Journal
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    • 제56권2호
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    • pp.419-430
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    • 2016
  • In this paper, we investigate the existence and uniqueness of positive solutions for three-point boundary value problem of nonlinear fractional q-difference equation. Some existence and uniqueness results are obtained by applying some standard fixed point theorems. As applications, two examples are presented to illustrate the main results.

EXISTENCE AND NONEXISTENCE OF POSITIVE SOLUTIONS TO NONLOCAL BOUNDARY VALUE PROBLEMS WITH STRONG SINGULARITY

  • Chan-Gyun Kim
    • East Asian mathematical journal
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    • 제39권1호
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    • pp.29-36
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    • 2023
  • In this paper, we consider φ-Laplacian nonlocal boundary value problems with singular weight function which may not be in L1(0, 1). The existence and nonexistence of positive solutions to the given problem for parameter λ belonging to some open intervals are shown. Our approach is based on the fixed point index theory.

PROPERTIES OF POSITIVE SOLUTIONS FOR THE FRACTIONAL LAPLACIAN SYSTEMS WITH POSITIVE-NEGATIVE MIXED POWERS

  • Zhongxue Lu;Mengjia Niu;Yuanyuan Shen;Anjie Yuan
    • 대한수학회지
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    • 제61권3호
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    • pp.445-459
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    • 2024
  • In this paper, by establishing the direct method of moving planes for the fractional Laplacian system with positive-negative mixed powers, we obtain the radial symmetry and monotonicity of the positive solutions for the fractional Laplacian systems with positive-negative mixed powers in the whole space. We also give two special cases.