数学季刊 ›› 2011, Vol. 26 ›› Issue (1): 77-84.

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具有p-Laplacian算子的二阶微分方程Picard边值问题

  

  1. Department of Mathematics, Guangdong University of Business Studies

  • 收稿日期:2007-03-29 出版日期:2011-03-30 发布日期:2023-05-11
  • 作者简介:LIU Yu-ji(1963- ), male, native of Suining, Hunan, a professor Guangdong University of Business Studies, Ph.D., engages in differential equations.
  • 基金资助:
    Supported by the Natural Science Foundation of Hunan Province(06JJ50008); Supported by the Natural Science Foundation of Guangdong Province(7004569);

Picard Boundary Value Problems of Second Order p-Laplacian Differential Equations 

  1. Department of Mathematics, Guangdong University of Business Studies
  • Received:2007-03-29 Online:2011-03-30 Published:2023-05-11
  • About author:LIU Yu-ji(1963- ), male, native of Suining, Hunan, a professor Guangdong University of Business Studies, Ph.D., engages in differential equations.
  • Supported by:
    Supported by the Natural Science Foundation of Hunan Province(06JJ50008); Supported by the Natural Science Foundation of Guangdong Province(7004569);

摘要: Sufficient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established, where [φ(x)] =(|x |p-2x) with p > 1. Our result is new even when [φ(x)] = x in above problem, i.e. p = 2. Examples are presented to illustrate the efficiency of the theorem in this paper.

关键词: solutions, second order p-Laplacian differential equation, two-point boundary
value problem,
fixed-point theorem

Abstract: Sufficient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established, where [φ(x)] =(|x |p-2x) with p > 1. Our result is new even when [φ(x)] = x in above problem, i.e. p = 2. Examples are presented to illustrate the efficiency of the theorem in this paper.

Key words: solutions, second order p-Laplacian differential equation, two-point boundary
value problem,
fixed-point theorem

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