## Boundary value problems of second order nonlinear functional difference equations.(English)Zbl 1198.39004

The author investigates the solvability of the nonlinear discrete boundary value problem with the Jacobi difference operator
$a_nu_{n+1}+b_nu_n+a_{n-1}u_{n-1}=f(n,u_{n+1},u_n,u_{n-1}), \quad n=0,1,\dots,N,$ and with the boundary condition $$\Delta u_0=A$$, $$u_{N+1}=B$$. It is supposed that the nonlinearity $$f$$ is of “variational character” and the existence results are proved using the mountain pass theorem. Note that in contrast to some related papers, the nonlinearity of $$f$$ is allowed to depend also on $$u_{n+1}$$.

### MSC:

 39A12 Discrete version of topics in analysis 34K10 Boundary value problems for functional-differential equations 39A10 Additive difference equations
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### References:

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