河北师范大学学报—

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刊名：河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
主办：河北师范大学
ISSN： 1000-5854
CN： 13-1061/N
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一类非线性项包含导数的p-Laplacian边值问题对称解的存在性

徐州工程学院数学与物理科学学院, 江苏徐州 221018
DOI： 10.13763/j.cnki.jhebnu.nse.2019.01.001

Existence of Symmetric Solutions to a p-Laplacian Boundary Value Problem with Nonlinear Term Involving Derivative

XUE Yimin, SU Ying

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摘要/Abstract

摘要：

研究了一维p-Laplacian动力方程
╭(φ_p(u'(t))'+h(t)f(t,u(t),u'(t))=0,
╰u(0)=u(1)=ω,u'(0)=-u'(1),t∈[0,1]
两点边值问题对称正解的存在性.利用锥压缩和锥拉伸不动点定理，得到了该边值问题一个对称正解的存在性定理.

Abstract：

In this paper,we study the following dynamic equation for the two-point BVPs with p-Laplacian in the form of
╭(φ_p(u'(t))'+h(t)f(t,u(t),u'(t))=0,
╰u(0)=u(1)=ω,u'(0)=-u'(1),t∈[0,1]
The existence of at least one positive symmetric solution is obtained by using the fixed point theorem of cone compression and expansion.

关键词

关键词： 边值问题 ; 对称解 ; p-Laplacian ; 不动点理论

Key words： boundary value problem ; symmetric solutions ; p-Laplacian ; fixed point theory

参考文献 16

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