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Zbl 1053.39003
Avery, Richard; Henderson, Johnny
Existence of three positive pseudo-symmetric solutions for a one dimensional discrete $p$-Laplacian. (English)
[J] J. Difference Equ. Appl. 10, No. 6, 529-539 (2004). ISSN 1023-6198

From the authors abstract. We apply the five functionals fixed point theorem to verify the existence of at least three positive pseudo-symmetric solutions for the three point boundary value problem $$\Delta \left( {g\left( {\Delta u\left( {t - 1} \right)} \right)} \right) + a\left( t \right)f\left( {u\left( t \right)} \right) = 0,$$ for $ t \in \left\{ {a + 1,...,b + 1} \right\} $ and $ u\left( a \right) = 0 $ with $ u\left( v \right) = u\left( {b + 2} \right) $ where $ g\left( v \right) = \left| v \right|^{p - 2} v,p > 1, $ for some fixed $ v \in \left\{ {a + 1,...,b + 1} \right\} $ and $ \sigma = \frac{{b + 2 + v}}{2} $ is an integer.
[B. G. Pachpatte (Aurangabad)]

MSC 2000:: *39A11 Stability of difference equations
39A12 Discrete version of topics in analysis
34B10 Multipoint boundary value problems

Keywords: five functionals fixed point theorem; positive pseudo-symmetric solutions; three point boundary value problem

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