Solvability of Boundary Value Problems for a Class of Third-Order Functional Difference Equations
DOI:
https://doi.org/10.5644/SJM.03.2.05Keywords:
Solution, third order functional difference equation, fixed-point theorem, growth conditionAbstract
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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References
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