• 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.

• 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.

• East Asian mathematical journal
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• 제39권1호
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• pp.43-50
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• 2023

This paper is concerned with the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. The fixed point index theorems are used for the main results.

• 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.

• 대한수학회지
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• 제49권1호
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• pp.153-164
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• 2012

In this paper, we study the existence, non-existence, and multiplicity of positive solutions for a coupled telegraph system using the xed-point theorem of cone expansion/compression type, the upper-lowe solutions method, and xed point index theory.

• 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.

• 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.

• East Asian mathematical journal
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• 제40권1호
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• pp.85-94
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• 2024

In this paper we study the existence and multiplicity of positive solutions for p-Laplacian problems with a singular weight. Proofs mainly make use of Global Continuation Theorem and Fixed Point Index argument.

• 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.