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He, Zhimin; Jiang, Xiaoming

Triple positive solutions of boundary value problems for \(p\)-Laplacian dynamic equations on time scales. (English) Zbl 1103.34012

J. Math. Anal. Appl. 321, No. 2, 911-920 (2006).
By using a triple fixed-point theorem, the authors prove the existence of at least three positive solutions of the \(p\)-Laplacian dynamic equation on a time scale \[ [\phi_{p}(u^{\Delta}(t))]^{\nabla}+g(t)f(u(t))=0,\quad t\in [0,T]_{\mathcal T}, \] satisfying the boundary conditions \[ u(0)-B_0(u^{\Delta}(0))=0, \quad u^{\Delta}(T)=0\quad {\text or} \quad u^{\Delta}(0)=0, \quad u(T)+B_1(u^{\Delta}(T))=0. \]
Reviewer: Sotiris K. Ntouyas (Ioannina)

Cited in 30 Documents

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
39A12 Discrete version of topics in analysis

Keywords:

time scale; \(p\)-Laplacian; boundary value problem; positive solution; fixed-point theorem
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\textit{Z. He} and \textit{X. Jiang}, J. Math. Anal. Appl. 321, No. 2, 911--920 (2006; Zbl 1103.34012)
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References:

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