Solvability of Boundary Value Problems for a Class of Third-Order Functional Difference Equations
Consider the boundary value problems consisting of the functional difference equation$$\Delta^3x(n)=f(n,x(n+2),x(n-\tau_1(n)),\dots,x(n-\tau_m(n))),\;\;n\in[0,T] $$ and the following boundary value conditions\[\begin{cases}x(0)=x(T+3)=x(1)=0,\\x(n)=\psi(n), \;n\in [-\tau,-1],\\x(n)=\phi(n),\;n\in [T...
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| Published in | Sarajevo journal of mathematics Vol. 3; no. 2; pp. 185 - 192 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
12.06.2024
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| Online Access | Get full text |
| ISSN | 1840-0655 2233-1964 2233-1964 |
| DOI | 10.5644/SJM.03.2.05 |
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| Summary: | Consider the boundary value problems consisting of the functional difference equation$$\Delta^3x(n)=f(n,x(n+2),x(n-\tau_1(n)),\dots,x(n-\tau_m(n))),\;\;n\in[0,T] $$ and the following boundary value conditions\[\begin{cases}x(0)=x(T+3)=x(1)=0,\\x(n)=\psi(n), \;n\in [-\tau,-1],\\x(n)=\phi(n),\;n\in [T+4,T+\delta].\end{cases}\]Sufficient conditions for the existence of at least one solution of this problem are established. We allow $f$ to be at most linear, superlinear or sublinear in the obtained results.
2000 Mathematics Subject Classification. 34B10, 34B15, 39A10 |
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| ISSN: | 1840-0655 2233-1964 2233-1964 |
| DOI: | 10.5644/SJM.03.2.05 |