Existence and Iteration of Solutions for a Multi-point Boundary Value Problem with a p-Laplacian Operator

De Xiang MA(1); Wei Gao GE(2)

Acta Mathematica Sinica, Chinese Series ›› 2008, Vol. 51 ›› Issue (3) : 447-456.

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Acta Mathematica Sinica, Chinese Series ›› 2008, Vol. 51 ›› Issue (3) : 447-456. DOI: 10.12386/A2008sxxb0052
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Existence and Iteration of Solutions for a Multi-point Boundary Value Problem with a p-Laplacian Operator

  • De Xiang MA(1); Wei Gao GE(2)
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Abstract

By employing Mawhin's continuation theorem,we obtain the existence of solutions and establish a corresponding iterative scheme for BVP, {(φ_p(u′))′+f(t,u) =0,0≤t≤1,u(0) = 0,u(1) =∑_(i=1)~(m-2)γ_iu(η_i). The upper and lower solutions method and monotone iterative technique are used.Fur- thermore,we impose sufficient conditions on f(t,u) which can guarantee the existence of nonnegative or nonpositive solutions even when f(t,u) is allowed to change sign.

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De Xiang MA(1); Wei Gao GE(2). Existence and Iteration of Solutions for a Multi-point Boundary Value Problem with a p-Laplacian Operator. Acta Mathematica Sinica, Chinese Series, 2008, 51(3): 447-456 https://doi.org/10.12386/A2008sxxb0052
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