Existence of positive solutions for certain partial difference equations
<p>We give some sufficient conditions for the existence of positive solutions of partial difference equation <mml:math alttext="$aA_m+1,n+1+bA_m,n+1+cA_m+1,n-dA_m,n+P_m,nA_m-k,n-l=0$"> <mml:mrow> <mml:mi>a</mml:mi><mml:msub> <mml:mi>A</mml:mi...
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| Format: | Article |
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| Language: | English |
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Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DDNS/2006/37103 |
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| description | <p>We give some sufficient conditions for the existence of positive solutions of partial difference equation <mml:math alttext="$aA_m+1,n+1+bA_m,n+1+cA_m+1,n-dA_m,n+P_m,nA_m-k,n-l=0$"> <mml:mrow> <mml:mi>a</mml:mi><mml:msub> <mml:mi>A</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:msub> <mml:mi>A</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo><mml:mi>c</mml:mi><mml:msub> <mml:mi>A</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:mo>−</mml:mo><mml:mi>d</mml:mi><mml:msub> <mml:mi>A</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo><mml:msub> <mml:mi>P</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>A</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>−</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo><mml:mn>0</mml:mn> </mml:mrow> </mml:math> by two different methods. </p> |
| format | Article |
| id | doaj-art-c55b0ccbfaec49c480c7c0933397e2c5 |
| institution | OA Journals |
| issn | 1026-0226 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-c55b0ccbfaec49c480c7c0933397e2c52025-08-20T02:18:39ZengWileyDiscrete Dynamics in Nature and Society1026-02262006-01-012006Existence of positive solutions for certain partial difference equations<p>We give some sufficient conditions for the existence of positive solutions of partial difference equation <mml:math alttext="$aA_m+1,n+1+bA_m,n+1+cA_m+1,n-dA_m,n+P_m,nA_m-k,n-l=0$"> <mml:mrow> <mml:mi>a</mml:mi><mml:msub> <mml:mi>A</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:msub> <mml:mi>A</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo><mml:mi>c</mml:mi><mml:msub> <mml:mi>A</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:mo>−</mml:mo><mml:mi>d</mml:mi><mml:msub> <mml:mi>A</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo><mml:msub> <mml:mi>P</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>A</mml:mi> <mml:mrow> <mml:mi>m</mml:mi><mml:mo>−</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo><mml:mn>0</mml:mn> </mml:mrow> </mml:math> by two different methods. </p>http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DDNS/2006/37103 |
| spellingShingle | Existence of positive solutions for certain partial difference equations Discrete Dynamics in Nature and Society |
| title | Existence of positive solutions for certain partial difference equations |
| title_full | Existence of positive solutions for certain partial difference equations |
| title_fullStr | Existence of positive solutions for certain partial difference equations |
| title_full_unstemmed | Existence of positive solutions for certain partial difference equations |
| title_short | Existence of positive solutions for certain partial difference equations |
| title_sort | existence of positive solutions for certain partial difference equations |
| url | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/DDNS/2006/37103 |