Positive solutions of BVPs for third-order nonlinear difference systems (Q1767777)
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scientific article; zbMATH DE number 2142330
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positive solutions of BVPs for third-order nonlinear difference systems |
scientific article; zbMATH DE number 2142330 |
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Positive solutions of BVPs for third-order nonlinear difference systems (English)
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8 March 2005
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The authors consider the discrete boundary value problem (BVP) of Dirichlet type for a nonlinear system \[ \Delta^3u_1(k) + f_1(u_1(k),u_2(k))= 0 \] \[ \Delta^3u_2(k) + f_2(u_1(k),u_2(k))= 0\;,\;0\leq k\leq T \] \[ u_1(0)=u_1(1)=u_1(T+3)=0=u_2(0)=u_2(1)=u_2(T+3) \] Sufficient conditions are given for the existence of one or two positive solutions using fixed point results of Leray-Schauder or Krasnosel'skii type.
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difference equation
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positive solution
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Dirichlet problem
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fixed point theorem
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Cone
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Nonlinear alternative
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discrete boundary value problem
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nonlinear system
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