Solvability of a class of generalized Neumann boundary value problems for second-order nonlinear difference equations (Q659506)
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scientific article; zbMATH DE number 5999625
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| English | Solvability of a class of generalized Neumann boundary value problems for second-order nonlinear difference equations |
scientific article; zbMATH DE number 5999625 |
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Solvability of a class of generalized Neumann boundary value problems for second-order nonlinear difference equations (English)
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23 January 2012
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Summary: This paper is motivated by [\textit{I. Rachůnková} and \textit{C. C. Tisdell}, Aust. J. Math. Anal. Appl. 3, No. 2, Article No. 6, 1--9 (2006; Zbl 1166.39009)] and with \textit{D. R. Anderson}, J. Math. Anal. Appl. 331, No. 1, 736--741 (2007; Zbl 1120.39014)]. New sufficient conditions for the existence of at least one solution of the generalized Neumann boundary value problems for second order nonlinear difference equations \[ \nabla \Delta x(k) = f(k, x(k), x(k+1)),\quad k \in [1, n - 1],\;x(0) = ax(1),\;x(n) = bx(n-1), \] are established.
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