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Zbl 1056.39024
Ma, Ruyun; Raffoul, Youssef N.
Positive solutions of three-point nonlinear discrete second order boundary value problem.
(English)
[J] J. Difference Equ. Appl. 10, No. 2, 129-138 (2004). ISSN 1023-6198

By applying a cone theoretical fixed point theorem, conditions are established for the existence of a positive solution to the three-point nonlinear second order boundary value problem $$\Delta^2 u(t-1)+a(t)f(u(t))=0, \quad t\in\{1,2,\cdots,N-1\},\ N\geq 2$$ $$u(0)=0,\qquad \alpha u(\eta)=u(N)$$ where $0<\eta< N$ and $0<\alpha<N/\eta.$
[Patricia J. Y. Wong (Singapore)]
MSC 2000:
*39A12 Discrete version of topics in analysis
39A11 Stability of difference equations
34B15 Nonlinear boundary value problems of ODE

Keywords: Cone theory; difference equation; positive solution; three-point nonlinear second order boundary value problem

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