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Triple positive pseudo-symmetric solutions of three-point BVPs for \(p\)-Laplacian dynamic equations on time scales. (English) Zbl 1139.34019

The authors are concerned with the three-point boundary value problem for \(p\)-Laplacian dynamic equations on time scales \(\mathbb{T}\) of the form
\[ (\phi_p(u^\Delta))^\nabla+h(t)f(t,u(t))=0\text{ for }t\in(0,T)_{\mathbb{T}} \]
with boundary conditions
\[ u(0)=0,\;u(\eta)=u(T), \]
where \(\mathbb{T}\) is symmetric in \([\eta,T]_{\mathbb{T}}\), \(\phi_p(u)=| u| ^{p-2}u\) with \(p>1\). The proof of the main result is based upon the five-functionals fixed-point theorem and a pseudo-symmetric technique. For related work see [D. Anderson, R. Avery, J. Henderson, J. Difference Equ. Appl. 10, No. 10, 889–896 (2004; Zbl 1058.39010)].
Reviewer: Ruyun Ma (Lanzhou)

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
39A10 Additive difference equations

Citations:

Zbl 1058.39010
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References:

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