• 제목/요약/키워드: fixed point index theorem

검색결과 9건 처리시간 0.019초

THE LEAST NUMBER OF COINCIDENCES WITH A COVERING MAP OF A POLYHEDRON

  • Jezierski, Jerzy
    • 대한수학회지
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    • 제36권5호
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    • pp.911-921
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    • 1999
  • We define the coincidence index of pairs of maps p, f : $\widetilde{X}$ $\rightarrow$ X where p is a covering of a polyhedron X. We use a polyhedral transversality Theorem due to T. Plavchak. When p=identity we get the classical fixed point index of self map of polyhedra without using homology.

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ALTERNATIVE PROOF OF EXISTENCE THEOREM FOR CERTAIN COMPETITION MODELS

  • Ahn, Inkyung
    • 충청수학회지
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    • 제13권1호
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    • pp.119-130
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    • 2000
  • We give alternative proof of the existence theorem for certain elliptic systems describing competing interactions with nonlinear di usion. The existence of positive solution depends on the sign of the principal eigenvalue of suitable operators of Schr$\ddot{o}$dinger type. If the sign of such operators are both positive, then system has a positive solution. The main tool employed is the fixed point index of compact operator on positive cones.

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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 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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    • 제28권1_2호
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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.

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR SINGULAR GENERALIZED LAPLACIAN PROBLEMS WITH A PARAMETER

  • Kim, Chan-Gyun
    • East Asian mathematical journal
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    • 제38권5호
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    • pp.593-601
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    • 2022
  • In this paper, we consider singular 𝜑-Laplacian problems with nonlocal boundary conditions. Using a fixed point index theorem on a suitable cone, the existence results for one or two positive solutions are established under the assumption that the nonlinearity may not satisfy the L1-Carathéodory condition.

POSITIVE PERIODIC SOLUTIONS OF IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS

  • LIU YUJI;XIA JIANYE;GE WEIGAO
    • Journal of applied mathematics & informatics
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    • 제19권1_2호
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    • pp.261-280
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    • 2005
  • We study the existence and nonexistence of positive periodic solutions of a non-autonomous functional differential equation with impulses. The equations we study may be of delay, advance or mixed type functional differential equations and the impulses may cause the existence of positive periodic solutions. The methods employed are fixed-point index theorem, Leray-Schauder degree, and upper and lower solutions. The results obtained are new, and some examples are given to illustrate our main results.